Seminars
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Historic
Torsionfree representations of Smith algebras
2024-04-24
Speaker: Samuel Lopes (CMUP, Univ. Porto)
We will discuss representations of the Smith algebra which are free of finite rank over a subalgebra which plays a role analogous to that of the (enveloping algebra of the) Cartan subalgebra of the simple Lie algebra \( \mathfrak{sl}_2 \). In the case of rank 1, we obtain a full description...
Standard monomials and Gröbner bases of positroid varieties
2024-04-03
Speaker: Daoji Huang (Univ. MInnesota, USA)
Influential work of Hodge from the 1940s led the way in using Gröbner bases to combinatorially study the Grassmannian. In this talk, we will follow Hodge's approach in order to investigate certain subvarieties called positroid varieties. Positroid varieties, introduced by Knutson-Lam-Speyer...
A review on the Eulerian ideal of a graph and its regularity
2024-03-13
Speaker: Gonçalo Varejão (CMUC, UC|UP PhD student)
Over the past fifty years, a trend in commutative algebra has been to explore families of homogeneous ideals, in the polynomial ring, linked to various combinatorial structures, such as graphs, hypergraphs and simplicial complexes.In this presentation, we focus on the Eulerian ideal of a...
A characterization of one-element commutation classes
2024-03-13
Speaker: Diogo Soares (CMUC, UC|UP PhD student)
A reduced word for a permutation of the symmetric group is its own commutation class if it has no commutation moves available. These words have the property that every factor of length 2 is formed by consecutive integers, but in general words of this form may not be reduced. In this...
Supercharacters: behind and beyond
2024-02-28
Speaker: Carlos André (CMUC & Univ. Lisboa)
Describing the conjugacy classes or irreducible characters of the unipotent upper triangular group over a finite field is known to be an impossibly difficult problem. Superclasses and supercharacters have been introduced (under the names of "basic varieties" and "basic characters") as...
The Keel-Tevelev embedding of \(M_{0,n}\)-bar
2023-07-12
Speaker: Jake Levinson (Simon Fraser Univ., Canada)
The moduli space \( M \)\( _{0,n} \)-bar describes n-marked stable curves of genus zero. It has a closed embedding into a product of projective spaces \( P^1 \times\cdots\times P^{n-3} \), due to Keel-Tevelev and Kapranov and involving the tautological "psi" and "omega" divisor...
On pseudo-Euclidean Lie algebras whose Levi-Civita product is left Leibniz
2023-07-05
Speaker: Said Benayadi (Univ. of Lorraine, France)
We study a class of Lie algebras which contains the class of quadratic Lie algebras and the class of Milnor Lie algebras, namely, Lie algebras endowed a pseudo-Euclidean metric such its Levi- Civita product is left Leibniz. We call them Levi-Civita left Leibniz Lie algebras LCLL for short....
A low-cost algorithm to determine spacecraft trajectories in CR3BP
2023-06-23
Speaker: Sirani M. Perera (Embry-Riddle Aeronautical University, USA)
The traffic within the Cislunar region continues to grow, yielding an increasing demand for efficient techniques to determine the trajectory of a satellite in the circular restricted three-body problem (CR3BP). In this talk, we introduce a novel technique that incorporates interpolation with...
Non symmetric Cauchy kernel, crystals and last passage percolation
2023-06-21
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
We use non-symmetric Cauchy kernel identities to get the law of last passage percolation (LPP) models in terms of Demazure characters (which are non symmetric polynomials) of a gl_n Lie algebra. The construction is based on restrictions of the Robinson-Schensted-Knuth (RSK)...
Blocks of endomorphism algebras of Young permutation modules for Hecke algebras
2023-06-21
Speaker: Stephen Donkin (Univ. of York, UK)
We consider a symmetric group acting on a set whose point stabilisers are products of smaller symmetric group (more precisely Young subgroups). The corresponding permutation module is called a Young permutation module. Familiar examples such as group algebras of symmetric groups,...
Varieties of algebras with derivations
2023-05-31
Speaker: Carla Rizzo (Univ. degli Studi di Palermo, Italy)
See attached file....
Chains and covers in K-theoretic multiplication rules
2023-04-26
Speaker: Mojdeh Tarighat (Univ. of Virginia, USA)
In 2020, Morse, Blasiak, and Seelinger introduced the K-theoretic Catalan functions as motivated by the search for a K-theoretic counterpart to the relationship between k-Schur structure constants and the complete flag variety. The authors conjectured that a subfamily, the closed k-Schur...
Statistical enumeration of groups by double cosets
2023-04-11
Speaker: Persi Diaconis (Stanford Univ., USA)
Let H and K be subgroups of a finite group G. This divides G into H-K double cosets. One may ask (1) how many double cosets are there? (2) what are their sizes? (e.g. pick g in G at random, what double coset is it likely to be in?) (3) Can one find 'nice names' for the double cosets? (4)...
Exact Borel subalgebras, good quotients and good subalgebras
2023-03-22
Speaker: Teresa Conde (Univ. of Stuttgart, Germany)
Exact Borel subalgebras of strandardly stratified algebras emulate the role of classic Borel subalgebras of complex semi-simple Lie algebras. Up to Morita equivalence, every standardly stratified algebra has an exact Borel subalgebra. By their recursive nature, standardly stratified algebras...
Moduli of twisted Higgs bundles as a degeneration of moduli of Lie algebroid connections
2023-03-08
Speaker: André Oliveira (CMUP, Univ. Trás-os-montes e Alto Douro)
Out of a given holomorphic Lie algebroid L on a compact Riemann surface X, one can consider a corresponding L-connection on a vector bundle over X. This naturally degenerates onto a (twisted) Higgs bundle on X. Via a generalization of the classical construction by Simpson of...
Crystals, and the Berenstein-Kirillov, cacti and related groups
2023-02-15
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
Berenstein and Kirillov have introduced and studied the group generated by the Bender-Knuth involutions modulo the relations they do satisfy on semi-standard tableaux of straight shape. Halacheva has generalized the Henriques-Kamnitzer cactus group to Dynkin diagrams of classical Cartan...
The palindromization map
2022-12-13
Speaker: Dominique Perrin (Univ. Gustave-Eiffel, Paris-Est, France)
The palindromization map has been defined initially by Aldo de Luca in the context of Sturmian words. It was extended to the free group of rank 2 by Kassel and Reutenauer. We extend their construction to arbitrary alphabets. We also investigate the suffix automaton and compact suffix...
A characterisation of Lie algebras using ideals and subalgebras
2022-12-07
Speaker: Xabier García Martínez (Univ. Vigo, Spain & Vrije Universiteit Brussel, Belgium)
In this talk we will state a result characterising the variety of Lie algebras amongst all varieties of non-associative algebras. More specifically, the variety of Lie algebras is the only variety that simultaneously satisfies the following two properties: every subalgebra of a free algebra...
Identities and bases in hypoplactic, sylvester and Baxter monoids
2022-11-30
Speaker: Duarte Ribeiro (CMA, Univ. Nova de Lisboa)
See the attached file....
Alternative algebras and maps preserving products equal to fixed elements
2022-11-16
Speaker: Douglas de Araujo Smigly (Univ. São Paulo, Brazil)
See the attached file...
The birth of Euclidean geometry (and mathematics) & the birth of non-Euclidean geometry
2022-07-18
Speaker: Dénes Nagy (Australian Catholic Univ., Melbourne, Australia)
TBA...
On the conjugation action for quantum GL(n)
2022-07-13
Speaker: Stephen Donkin (Univ. of York, UK)
The algebra of polynomial functions on n by n complex matrices that are constant on conjugacy classes is the free polynomial algebra on the functions giving the coefficients of the characteristic polynomial. Here we give a similar description of the algebra of invariants C(G), for the action...
Ramsey theory for infinite words
2022-07-06
Speaker: Manuel Silva (Univ. Nova de Lisboa)
We will discuss several ramsey-type results in combinatorics on words. In one of the results, it is proved that the existence of powers or anti-powers is an unavoidable regularity for sufficiently long words. An abelian version, where we count the frequency of each letter, is conjectured to...
Characterization of maps
2022-06-08
Speaker: Bruno Leonardo Macedo Ferreira (Federal University of Technology-Paraná, Brazil)
See the attached file....
The combinatorics of Kostka polynomials
2022-05-04
Speaker: Cédric Lecouvey (Univ. Tours, France)
In representation theory of the Lie algebras, each irreducible representation decomposes into weight spaces. The dimensions of these subspaces can be computed via the Weyl character formula and admit interesting quantizations. The polynomials so obtained have a simple definition and numerous...
Functorial approach to rank functions
2022-03-30
Speaker: Teresa Conde (Univ. of Stuttgart, Germany)
Motivated by the work of Cohn and Schofield on Sylvester rank functions on rings, Chuang and Lazarev have recently introduced the notion of a rank function on a triangulated category. A rank function is a nonnegative real-valued, additive, translation-invariant function on the objects of a...
Symmetric decompositions, triangulations and real-rootedness
2022-02-16
Speaker: Eleni Tzanaki (Univ. Crete, Greece)
A triangulation of a simplicial complex Δ is said to be uniform if the f-vector of its restriction to a face of Δ depends only on the dimension of that face. The notion of uniform triangulation was introduced by Christos Athanasiadis in order to conveniently unify many well...
Injectivity of induction in Lie theory
2022-01-26
Speaker: Thomas Gerber (EPFL, Lausanne, Switzerland)
Given two isomorphic representations of a simple lie algebra over ℂ induced from two irreducible representations V and W of a parabolic subalgebra, what can be said about V and W? In this talk, we consider the case of the general linear and symplectic Lie algebras. We show that the...
Relative dominant dimension and quality of split quasi-hereditary covers.
2022-01-19
Speaker: Tiago Cruz (Univ. Stuttgart, Germany)
Dominant dimension of a finite-dimensional algebra A is a homological invariant measuring the connection between module categories A-mod and B-mod, where B is the endomorphism algebra of a faithful projective-injective A-module.In this talk, we will discuss generalisations of dominant...
Potent preservers of incidence algebras
2022-01-12
Speaker: Mykola Khrypchenko (Univ. Federal de Santa Catarina, Brazil)
Let X be a finite connected poset and F a field. Denote by I(X,F) the incidence algebra of X over F. We describe bijective linear maps from I(X,F) to I(X,F) which preserve k-potency, where k is a fixed integer greater than 1. The case k=2 (idempotent preservers) is treated for arbitrary F,...
On simple 15-dimensional Lie algebras in characteristic 2
2021-11-17
Speaker: Pasha Zusmanovich (Univ. Ostrava, Czech Republic)
Classification of finite-dimensional Lie algebras over a field of characteristic 2 is a widely open problem. We will discuss a certain 15-dimensional such algebra, first appearing in the works of Skryabin. It possesses a number of interesting properties which may be typical for a certain...
The regularity of Eulerian ideals
2021-11-10
Speaker: Jorge Sentieiro Neves (CMUC, Univ. Coimbra)
The Eulerian ideal of a graph establishes yet another bridge between algebra and combinatorics. It encodes much information about the graph: its generators can be related to the Eulerian subgraphs with an even number of edges and, for a fixed monomial order, the associated standard...
Families of polytopes with rational linear precision in higher dimensions
2021-11-03
Speaker: Eliana Duarte (CMUP, Univ. Porto)
Polytopes with rational linear precision are of interest in the Geometric Modeling community because of their approximation properties and it is an open question to classify them in dimension d > 2. This classification question is closely related to discrete statistical models with...
On the lattice of restricted subalgebras of a restricted Lie algebra
2021-10-27
Speaker: Pilar Paez-Guillán (Univ. Santiago de Compostela, Spain)
Historically, the question of how far the properties of the subgroup lattice of a group G determine those of G has been extensively studied. Similar questions have been formulated for Lie algebras and restricted Lie algebras.In this talk, we will give a general characterization for...
Orthogonal symmetric matrices and joins of graphs
2021-09-22
Speaker: Helena Smigoc (Univ. College Dublin, Ireland)
We ask when is the join of two (possibly disconnected) graphs G and H the pattern of an orthogonal symmetric matrix. A notion of compatibility for multiplicity matrices gives rise to a necessary condition. To address sufficiency, we introduce generic realisability that generalises the...
Eulerian polynomials via the Weyl algebra action
2021-07-07
Speaker: José Agapito Ruiz (Univ. Lisboa)
We obtain a generalization of the Worpitzky identity and new recursive formulas for a family of polynomials that include the classical Eulerian polynomials, using the action of the Weyl algebra on the geometric series and the framework of rook placements on Ferrers boards for combinatorial...
Polynomial identities and central polynomials: their growth
2021-06-23
Speaker: Carla Rizzo (Univ. Palermo, Italy)
A central polynomial of an algebra A is a polynomial f in non-commutative variables that takes central values when evaluated in A. In case it vanishes in A, f is called a polynomial identity of A, otherwise f is a proper central polynomial of A. The purpose of this talk is to survey some old...
Symplectic left and right keys - Type C Willis' direct way
2021-06-23
Speaker: João Miguel Santos (PhD student, CMUC)
The right and left key maps for Kashiwara-Nakashima tableaux are used to describe type C Demazure and opposite Demazure crystals, respectively. For instance, Fu-Lascoux non-symmetric Cauchy kernels expand into products of opposite Demazure characters and Demazure atoms. These key maps are...
Torsion pairs and Ringel duality for Schur algebras
2021-06-09
Speaker: Karin Erdmann (Univ. of Oxford, UK)
A finite-dimensional quasi-hereditary algebra has a Ringel dual which is again quasi-hereditary. For blocks of both the classical and quantum Schur algebras S(2,r) and Sq(2,r) we show they are Morita equivalent to their Ringel duals if they contain 2pk simple modules. This uses a...
A uniform action of the dihedral group \(\mathbb{Z}_2 \times D_3\) on Littlewood-Richardson coefficients
2021-05-12
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
The Littlewood-Richardson (LR) coefficient symmetries under the action of the dihedral group \( \mathbb Z_2\times D_3 \) of order twelve refers to the invariance of LR coefficients, under an action of that group on LR triples of partitions, the partition-triples indexing LR...
Smooth representations of groups associated with algebras defined over non-archimedean fields
2021-04-28
Speaker: João Dias (CEAFEL, Univ. Lisboa)
In this talk, I will show a description of the irreducible smooth representations of algebra groups, unit groups of a split basic algebra and involutive algebra groups over a non-archimedean field (for example the p-adic field). In particular, I will discuss the admissibility and...
Shifted Bender-Knuth moves and a shifted Berenstein-Kirillov group
2021-01-13
Speaker: Inês Rodrigues (CEAFEL, Univ. Lisboa)
The Bender-Knuth moves on Young tableaux are well-known involutions, namely, they are used in a combinatorial proof that the Schur functions are symmetric, as well as in alternative proofs of the classic Littlewood-Richardson rule. The group generated by these involutions, modulo the...
Quasihereditary algebras with exact Borel subalgebras
2020-12-09
Speaker: Teresa Conde (Univ. Stuttgart, Germany)
Exact Borel subalgebras of quasihereditary algebras emulate the role of "classic" Borel subalgebras of complex semisimple Lie algebras. Not every quasihereditary algebra A has an exact Borel subalgebra. However, a theorem by Koenig, Külshammer and Ovsienko establishes that...
On the combinatorics of linear dependencies of 0-1 vectors
2020-11-18
Speaker: Ilda Perez Fernandez Silva (Univ. Lisboa)
It was recently proven (J. Geelen, B. Gerards, G. Whittle) that linear dependence over any given finite field can be characterized combinatorically, via matroids, in terms of a finite number of excluded subconfigurations (minors). It is known that representability over the reals can not be...
Finite fields meet Markov chains
2020-11-11
Speaker: Persi Diaconis (Stanford Univ., USA)
In joint work with Jimmy He and Marty Isaacs we have been exploring a curious interface between Galois theory and Probability. The problems are easy to state: Consider first Z/pZ. A random walk takes x to x+1 or x-1 with probability 1/2. As I will explain, it takes order p^2 steps (N&S)...
Cactus group actions on shifted tableau crystals and a shifted Berenstein-Kirillov group
2020-07-01
Speaker: Inês Rodrigues (CEAFEL, Univ. Lisboa)
Recently, Gillespie, Levinson and Purbhoo introduced a crystal-like structure for shifted tableaux, called the shifted tableau crystal. We introduce a shifted version of the crystal reflection operators, which coincide with the restrictions of the shifted Schützenberger involution to...
A non-Levi branching rule in terms of Littelmann paths
2020-05-20
Speaker: Jacinta Perez Gavilan Torres (Institute of Mathematics, Polish Academy of Sciences)
We will give an introduction to the Littelmann path model for representations of simple Lie algebras, highlighting its most important applications and connectionsto algebraic combinatorics. Then we will present a non-Levi branching rule in terms of Littelmann paths. This is joint work with...
Mirror symmetry on the Hitchin system
2020-01-24
Speaker: Emilio Franco Gomez (CAMGSD, IST, Lisboa)
We will provide an overview of Mirror Symmetry phenomena occurring in the framework of the Hitchin system....
Branes on the Hitchin system via torsion bundles
2020-01-24
Speaker: André Oliveira (CMUP & UTAD)
We study the fixed point loci on the moduli space M of GL(n,C)-Higgs bundles (over a curve) for the action of tensorization by a torsion line bundle of order n. This is a hyperholomorphic loci which can be equipped with a hyperholomorphic sheaf, hence is constitutes a BBB-brane on M. Such a...
The feasible region for consecutive occurrences of large permutations
2020-01-22
Speaker: Raúl Penaguião (Univ. Zürich, Switzerland)
The study of patterns in permutations has steadily gathered interest in combinatorics. The notion of classical pattern has been well studied so far, for instance giving rise to the limit object of a permuton. The proportions of these patterns takes values between zero and one and the precise...
Combinatorics and moduli of line bundles on stable curves
2020-01-15
Speaker: Ana Margarida Melo (CMUC, Univ. Coimbra)
The moduli space of line bundles on smooth curves of given genus, the so called universal Jacobian, has a number of different compactifications over the moduli space of stable curves. These compactificatons have very interesting combinatorial properties, which can be used to describe their...
A walk from D-modules to distribution theory through the conjugation functor
2020-01-08
Speaker: Teresa Monteiro Fernandes (CMAFcIO, Univ. Lisboa)
I will recall Kashiwara's conjugation functor from the derived category of regular holonomic D-modules over a complex manifold to the derived category of regular holonomic D-modules on the complex conjugate manifold \bar{X}, which he proved to be an equivalence of categories thanks to the...
The Picard group of the universal G-bundle over the moduli stack of pointed curves
2019-10-16
Speaker: Filippo Viviani (CMUC/Roma Tre)
I will report on a joint work (in progress) with R. Fringuelli where we compute the Picard group of the moduli stack parametrizing pairs consisting of a smooth pointed curve C together with a G-principal bundleon C, for a given reductive algebraic group G....
On nilpotent elements
2019-09-18
Speaker: Miguel Gómez Lozano (Univ. Málaga, Spain)
See the attached file....
The Schützenberger involution on Kashiwara-Nakashima tableaux
2019-06-26
Speaker: João Miguel Santos (CMUC, Univ. Coimbra)
The Schützenberger involution, due to Schützenberger, originally appeared in type A root system, using the model of semistandard Young tableaux. In this talk, we present a type C realization of the Schützenberger involution using the model of Kashiwara-Nakashima tableaux....
Algebraic and geometric classification of nilpotent Tortkara algebras
2019-06-12
Speaker: Mykola Khrypchenko (Univ. Federal de Santa Catarina, Brazil)
We classify all nilpotent Tortkara algebras of dimension 6 over the field of complex numbers. We also determine the rigid algebras and irreducible components of the variety of such algebras. This is a joint work with Ilya Gorshkov (Sobolev Institute of Mathematics) and Ivan Kaygorodov...
Parametric Presburger arithmetic
2019-06-12
Speaker: Tristram Bogart (Univ. de los Andes, Colombia)
Parametric Presburger arithmetic concerns families of sets defined using quantifiers and Boolean combinations of formulas of the form a(t)·x ≤ b(t), where a(t) ∈ Z[t] d , b(t) ∈ Z[t]. In the quantifier-free these formulas represent sets of integer points in families of...
Normally ordered forms of powers of differential operators
2019-06-05
Speaker: Samuel Lopes (CMUP, Univ. Porto)
See the attached file....
On the dimension formula for Goldie's uniform dimension
2019-05-29
Speaker: Christian Lomp (Univ. Porto)
A classical (right) ring of fractions of a ring R is an overring Q(R) of R such that any non-zero divisor of R is invertible in Q(R) and any element of Q(R) is of the form ab^{-1} for a and b elements of R with b a non-zero divisor. Oystein Ore proved in the 30s that a (non-commutative)...
Recent thoughts about the NIEP
2019-05-15
Speaker: Charles Johnson (College of William and Mary, Williamsburg, USA)
We discuss 3 topics about the nonnegative inverse eigenvalue problem about which recent progress has been made. These include 1) ruling out certain spectra for the 5-by-5 S-NIEP; 2) Jordan structure for realizable spectra with repeated eigenvalues; and 3) the doubly stochastic single...
Feedback invariants of series connected systems and LR coefficients
2019-05-15
Speaker: Marija Dodig (Univ. Lisboa)
In this talk we shall describe the possible feedback invariants of linear systems obtained as a result of series connections of two linear systems. This corresponds to a completion problem for matrices. We solve the problem in a generic case, and we conjecture general solution. It turns...
Rees algebras of modules
2019-04-10
Speaker: Ana Luísa Correia (Academia Militar and CEAFEL - FCUL)
The Rees algebra of an ideal may be seen as a coordinate ring of a projective variety and it plays an important role in the study of algebraic singularities. Many parts of this theory can also be extended to the case of filtrations ideals or modules, as well to the case of the multi-Rees...
On finite simple quotients of triangle groups
2019-02-27
Speaker: Claude Marion (CMUP, Univ. Porto)
See the attached file...
The 2-representation theory of Soergel bimodules of finite Coxeter type: a road map to the complete classification of all simple transitive 2-representations.
2019-01-23
Speaker: Marco Mackaaij (Univ. Algarve)
I will recall Lusztig's J-categories, which are fusion categories obtained from the perverse homology of Soergel bimodules. For example, for finite dihedral Coxeter type this fusion category is the semisimplified quotient of the module category of quantum so(3) at a root of unity, which...
Tree oriented pullbacks
2019-01-16
Speaker: Flávio Ulhoa Coelho (Univ. São Paulo, Brazil)
See the attached file....
Homological invariants of blocks of Schur algebras
2018-12-06
Speaker: Steffen Koenig (Univ. Stuttgart, Germany)
Let S(n,r) be a classical or quantised Schur algebra with n ≥ r. Totaro determined the global dimension of classical S(n,r) and Donkin extended this result to quantum S(n,r). Ming Fang and I have determined the dominant dimension (which in some sense measures the strength of Schur-Weyl...
Kippenhahn's Theorem
2018-11-28
Speaker: Stephan Weis (CMUC, Univ. Coimbra)
The numerical range of a matrix is a convex subset of the plane of complex numbers (Toeplitz 1919, Hausdorff 1919) and equals the convex hull of a real algebraic curve (Kippenhahn 1951, Chien and Nakazato 2010). An interesting higher-dimensional analogue would be to write the joint...
Lattice decomposition of modules and decomposition of categories
2018-11-21
Speaker: Pascual Jara (Univ. de Granada, Spain)
The decomposition of a module M in a direct sum M=M1+M2 does not produce, in general, a decomposition of the lattice L(M) of all submodules in a direct product of lattices L(M)=L(M1)xL(M2). When this happens we say M=M1+M2 is a lattice decomposition. These particular decompositions have...
Leibniz algebras with invariant forms
2018-10-31
Speaker: Said Benayadi (Univ. de Lorraine, Metz, France)
In the case of Lie algebras, the left (resp. right) invariance of bilinear forms is equivalent to the invariance (or associativity) of these forms. However, it is not the case for Leibniz algebras.In this talk, we will give some results on the structures of Leibniz algebras which are...
Asymptotic theory of set partitions: a representation theory agenda
2018-10-24
Speaker: Jocelyn Lochon (Univ. Lisboa)
See the attached file....
Nonassociative products in nonassociative algebras with involution
2018-10-03
Speaker: Jose Ramón Brox López (CMUC)
Starting from the variety of associative, Lie, Jordan, or alternative algebras with involution (or involutive automorphism), we classify all the formal bilinear products of the formaxy+bx*y+cxy*+dx*y*+Ayx+Byx*+Cy*x+Dy*x*,formed with the help of the original product and the involution *...
On the Clebsch-Gordan problem in positive characteristic
2018-07-05
Speaker: Stephen Donkin (Univ. of York, UK)
This is joint work with Samuel Martin. Consider the special linear group G of degree 2, over the complex numbers. There is one rational irreducible G-module V(r) for each non-negative integer r. The module V(r) has dimension r+1 and may be realised as the rth symmetric power of the...
Tree conjecture on graphs and more colourings in polytopes
2018-06-29
Speaker: Raul Penaguião (Univ. Zurich, Switzerland)
We will talk about some chromatic invariants in graphs and polytopes, and see what are the consequences of a nice description of the kernel of these chromatic maps in important problems like the tree conjecture. We will see that the most general version of this problem is in the realm of...
Totally nonnegative unitriangular Toeplitz matrices and k-Schur functions
2018-06-21
Speaker: Cédric Lecouvey (Univ. François Rabelais, Tours, France)
The talk will focus on effective parametrisations of unitriangular Toeplitz matrices. We will first recall Thoma's parametrisation for the infinite matrices. Next, for matrices of rank k, we will see how one can recover Rietsch's parametrisation by k-tuple of nonnegative reals from the...
Supercharacters for algebra groups and their geometric relations
2018-06-06
Speaker: João Dias (Univ. Lisboa)
Given any algebra group over any finite field one has a supercharacter theory constructed by P. Diaconis and I.M. Isaacs. And we may ask three questions:- How the supercharacter theory behaves with respect to change of field (i.e. finite field extensions)- Exists an object that contains all...
Supercharacters, Schur rings and association schemes
2018-05-30
Speaker: Carlos André (Univ. Lisboa)
In this talk, we describe and illustrate the connection of supercharacter theories of finite groups with Schur rings and association schemes, and we discuss possible generalisations to the context of (infinite) topological groups, in particular of totally disconnected compact and locally...
On the profinite topology on solvable groups
2018-05-23
Speaker: Khadijeh Alibabaei (CMUP, Univ. Porto)
We show that the wreath product of a finitely generated abelian group with a polycyclic group is a LERF group. This theorem yields as a corollary that the finitely generated free metabelian group is LERF, a result due to Coulbois.We also show that the finitely generated free solvable group...
Supercharacters of unitriangular groups and ramification graphs
2018-05-02
Speaker: Filipe Gomes (Univ. Lisboa)
Supercharacter theories are generalizations of the usual character theory of a group. In this talk, we present the basics of supercharacter theory, emphasizing the supercharacter theory of the unitriangular groups and its combinatorial interpretations. In the second part of the talk, we...
Identities in plactic and related monoids
2018-04-18
Speaker: António Malheiro (Univ. Nova de Lisboa)
The plactic monoid is a fundamental algebraic object which captures a natural monoid structure carried by the set of combinatorial objects of semistandard Young tableaux. Other monoids arise in a similar way by considering different combinatorial objects: the hypoplactic monoid...
Sets of operators determined by the numerical range
2018-03-19
Speaker:
Janko Bracic (Univ. of Ljubljana, Slovenia)
See the attached file....
On the regularity of the vanishing ideals of graphs
2018-03-07
Speaker: Jorge Neves (CMUC, Univ. Coimbra)
In 2011, Renteria, Simis and Villarreal introduced a new class of binomial ideals associated to graphs. One associates to a simple graph, G, the vanishing ideal of a subset of a projective space over a finite field, parameterized by the edges of the graph. Although originally these ideals...
The intricacies of algebraic power series
2018-02-07
Speaker: Herwig Hauser (Univ. of Vienna, Austria)
A formal power series h(x) = sum a_n x^n is called algebraic if it satisfies a polynomial equation with coefficients in K[x]. Typical examples are rational series like (1+x)^(-1) or roots of polynomials like sqrt(1+x). In characteristic 0, it is an open problem to characterize the...
From Brauer trees to surface algebras
2018-01-24
Speaker: Karin Erdmann (Univ. of Oxford, UK)
We describe algebras constructed from graphs, and from surface triangulations, starting with Brauer tree algebras. We discuss how J. A. Green's walk around the Brauer tree generalizes....
Quantum chaology in phase space through the Wigner transform
2018-01-10
Speaker: Luís Pereira (Univ. Lisboa)
The Wigner function is one of the five major equivalent formulations of Quantum Mechanics. The others being Schrödinger's Heisenberg's, Feynman's path integral and the Density Operator. The study of the quantization of classically chaotic systems in the 70's led to the generalization of...
Right-angled Artin groups: commensurability classification and subgroup intersection problem
2017-12-13
Speaker: Alexander Zakharov (CMUP, Univ. Porto)
The class of right-angled Artin groups (RAAGs) is a prominent class of groups which is widely studied in different branches of mathematics and computer science. Two groups are called commensurable if they have isomorphic subgroups of finite index. In the first part of the talk I will present...
The Kostant form of \(\mathfrak U(sl^+_n)\) and the Borel-Schur algebra
2017-11-29
Speaker: Ana Paula Santana (CMUC, Univ. Coimbra)
See the attached file...
The number of parking functions with center of a given length
2017-11-29
Speaker: Rui Duarte (Univ. Aveiro)
Let 1\leq r\leq n and suppose that, when the Depth-first Search Algorithm is applied to a given rooted labelled tree on n+1 vertices, exactly r vertices are visited before backtracking. Let R be the set of trees with this property. We count the number of elements of R.For this purpose, we...
On the combinatorics of a family of generalized Catalan triangles
2017-11-15
Speaker: Angela Mestre (Univ. Lisboa)
We generalize Aigner's array of the ballot numbers to a family of Riordan arrays. The entries of these generalized Catalan triangles are homogeneous polynomials in two variables which interpolate between the ballot numbers and the binomial coefficients. We show that the generalized Pascal...
On the representation theory of the Infinite Unitriangular group
2017-10-18
Speaker: Jocelyn Lochon (Univ. Lisboa)
Let U(q) denote the set of infinite nilpotent matrices over the finite field with q elements, called infinite unitriangular group. It is a wild group (not type I), thus the irreducible representation do not admit any reasonable parametrization.Nevertheless the set of all characters...
A new signature of quantum phase transitions from the numerical range
2017-07-10
Speaker: Stephan Weis (Université libre de Bruxelles, Belgium)
A quantum phase transition is a ground state phenomenon in an infinite lattice model with various defining key properties. We focus on two of them and point out their signatures in finite lattice models: Non-analyticity of the ground state energy and strong variation of the entropy of...
On the Kantor product
2017-06-28
Speaker: Ivan Kaygorodov (Univ. Federal do ABC, Santo André, Brazil; Siberian State Aerospace Univ., Krasnoyarsk, Russia)
Kantor defined the conservative algebras as an generalization of Lie and Jordan algebras. There are many relations between conservative algebras and other non-associative algebras. We will talk about some classical papers of Kantor and some new results obtained in some joint work with Yu....
Semisimple Hopf actions and factorization through group actions
2017-05-31
Speaker: Deividi Pansera (Univ. Porto)
See the attached file....
Extensions of Herstein's theory on Jordan (and Lie structures) to more general associative systems
2017-05-24
Speaker: Fernando Montaner (Univ. Zaragoza, Spain)
In the mid 1950s Herstein's opened a field of research which had as its aim the study of the structures of Lie and Jordan algebras that can be obtained from an associative algebra (possibly, with an involution) by endowing it with the Lie product ([xy]=xy-yx) or the Jordan product...
Combinatorics and HOMFLYPT invariants of knots
2017-05-17
Speaker: Marko Stosic (IST, Lisboa)
HOMFLYPT invariants are one of the most important and general invariants in the study of the topological properties of knots. Apart from the purely knot-theoretic interest, they are related to numerous different areas of mathematics and physics, including representation theory, operator...
Polytopes, slack ideals and psd-minimality
2017-04-26
Speaker: João Gouveia (CMUC / Univ. Coimbra)
The slack ideal is an algebraic object that codifies the geometry of a polytope. This notion was motivated by the study of psd-minimality of polytopes: A d-polytope is said to be psd-minimal if it can be written as a projection of a slice of the cone of d+1 by d+1 positive semidefinite...
How to extend an edge colouring?
2017-04-19
Speaker: António Girão (Univ. Cambridge, UK)
See attached pdf file....
Combinatorics in minimal case completions of matrix pencils
2017-04-05
Speaker: Marija Dodig (Univ. Lisboa)
In this talk we shall present some combinatorial tools in resolving matrix pencil completion problems. Also, we shall explain the concept of minimal completions, and present the solution of the general matrix pencil completion problem in the minimal case....
Solution of a matrix problem coming from differential equations
2017-04-05
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg, USA)
TBA...
Hopf algebras and Ore extensions
2017-03-29
Speaker: Christian Lomp (Univ. Porto)
Enveloping algebras of Lie algebras are typical examples of Hopf algebras. Some of them can be presented as iterated Ore extensions, which are a sort of non-commutative polynomial rings. This raises the natural question as to which Ore extensions over a Hopf algebras R admit a Hopf algebra...
Connection techniques for the study of the structure of algebraic objects
2017-03-15
Speaker: José M. Sánchez (CMUC)
After recalling classical results in order to place our work, we summarize the evolution of the connection techniques and its useful applications to the study of split decompositions. By making use of these techniques, we focus our attention on the study of the structure and the simplicity...
Dual enrichment and Isbell Duality
2017-01-30
Speaker: Martin Hyland (Univ. of Cambridge, UK)
The category of presheaves on a given small category is enriched in the category of presheaves on its opposite. This piece of Category Theory folklore is under appreciated perhaps because it is not clear what to do with it. I shall discuss versions of this phenomenon and how it looks from...
Sign patterns of coefficients of power series associated with the spectra of positive matrices
2017-01-30
Speaker: Thomas Laffey (Univ. College Dublin, Ireland)
See attached pdf file....
Internal Schensted insertion and tableau-switching involution
2017-01-18
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
Robinson-Schensted insertion and Sch\"utzenberger jeu de taquin are central operations in algebraic combinatorics with deep applications in other areas. Knuth transformations on words explain how they are related by showing what they do on words. This allows to replace insertion...
The ADR algebra and other strongly quasihereditary algebras
2017-01-04
Speaker: Teresa Conde (Univ. Stuttgart, Germany)
Quasihereditary algebras were introduced by Cline, Parshall and Scott in order to deal with highest weight categories arising from Lie theory. A prototype for quasihereditary algebras are the Schur algebras.Given a finite-dimensional algebra A, we may associate to it a special endomorphism...
Derivations and generalized derivations of non-associative algebras
2016-12-14
Speaker: Ivan Kaygorodov (Univ. Federal do ABC, Brazil)
A famous theorem of Jacobson talks about the nilpotency of any finite dimensional Lie algebra with an invertible derivation. We will discuss about some generalizations of this theorem for the case of Leibniz derivations and other non-associative algebras. In particular, we will talk about...
Finite dimensional Poisson algebras
2016-12-07
Speaker: Mohamed Boucetta (Univ. Cadi-Ayyad, Marrakech, Morocco)
See attached file. ...
Topological mirror symmetry for parabolic Higgs bundles
2016-11-30
Speaker: André Oliveira (CMUP, Univ. Porto)
See attached file....
Extreme supercharacters of the infinite unitriangular group
2016-11-23
Speaker: Carlos André (CEAFEL, Univ. Lisboa)
We define extreme supercharacters of the infinite unitriangular group, introduce the ramification scheme associated with the classical supercharacter theories of the finite unitriangular groups and describe how extreme supercharacters of the infinite unitriangular group appear as weak limits...
Explicit Schoen Surfaces
2016-10-19
Speaker: Carlos Rito (Centro de Matemática da Universidade do Porto)
See the attached file....
First degree cohomology of Specht modules and extensions of symmetric powers
2016-10-12
Speaker: Stephen Donkin (Univ. of York, UK)
This is joint work with H. Geranios. We compute the dimensions of the first degree cohomology of all Specht modules for symmetric groups in characteristic different from 2. Our method is to make a comparison with extension groups for general linear groups and Borel subgroups and then make a...
Saturated numerical semigroups
2016-09-28
Speaker: Manuel B. Branco (Univ. Évora)
See the attached file....
Conjecture of Alon-Tarsi
2016-07-20
Speaker: Carlos Gamas (Univ. Coimbra)
See the attached file...
Monochromatic configurations in finite colorings of N
2016-07-06
Speaker: Joel Moreira (Ohio State Univ., USA)
Is it possible to color the natural numbers with finitely many colors, so that whenever x and y are of the same color, their sum x+y has a different color? A 1916 theorem of I. Schur tells us that the answer is *no*. In other words, for any finite coloring of N, there exist x and y such that...
A preaction of the 0-Hecke monoid
2016-06-29
Speaker: Ana Paula Santana (CMUC, Univ. Coimbra)
I will construct a preaction of the Hecke monoid on the category of rational modules for the quantum negative Borel subgroup of the quantum general linear group. I will also show that this preaction induces a preaction on the category of modules for the quantised Borel-Schur algebra. This...
Invariants and Hochschild cohomology of rings of differential operators in one variable
2016-05-04
Speaker: Samuel Lopes (Univ. Porto)
A polynomial h in the variable x determines the derivation h(d/dx) of the polynomial ring F[x] and, together with the multiplication by x operator, it generates a noncommutative algebra A_h whose elements can be written as differential operators on h(d/dx) with coefficients in F[x]. I will...
A discrete nonsymmetric variant of the Minkowski Convex Body Theorem
2016-04-27
Speaker: Stanislav Kondratyev (CMUC)
In this talk we discuss a discrete version of the Minkowski Convex Body Theorem for convex integer polygons on the plane. The theorem states that given a sublattice of the integer lattice, any such polygon with sufficiently many vertices contains at least one point of the sublattice. An...
An overview over conjugacy in semigroups
2016-04-13
Speaker: António Malheiro (Univ. Nova de Lisboa, CMA)
When generalizing a concept, it is sometimes tempting to think that there should be one correct, or even preferred, generalization. Since semigroup theory is a vast subject, intersecting many areas of pure and applied mathematics, it is probably not reasonable to expect a one-size-fits-all...
Multiplicity lists for symmetric matrices whose graphs have many edges
2016-04-06
Speaker: Zhang Yulin (Univ. Minho)
We characterize the possible lists of multiplicities occurring among the eigenvalues of real symmetric (or Hermitian) matrices whose graph is one of Kn, Kn less an edge, or both possibilities for Kn less two edges. The lists are quite different from those for trees. Some construction...
BV Formality
2016-03-30
Speaker:
Ricardo Campos (Univ. Zurich, Switzerland)
To a smooth manifold one can associate the Lie algebras of multivectorfields and multidifferential operators. Relating these two led Kontsevich to his famous formality theorem that establishes the deformation quantization of Poisson manifolds.In this talk we will see that if the...
n-Algebras admitting a multiplicative basis
2016-03-09
Speaker: José M. Sánchez Delgado (CMUC)
See the attached file....
Geometry of numerical range of linear pencils
2016-02-17
Speaker: Fatemeh Esmaeili Taheri (CMUC)
See the attached file....
The Universal Generalization Problem. Euclid's mathematical solutions and contemporary formal accounts
2016-01-18
Speaker:
Pierluigi Graziani (University of Chieti-Pescara - Italy)
The goal of my talk is to analyze different contemporary foundations of Euclid's Geometry [1], compare them with each other and with the philological studies of ancient texts. In particular, I will analyze how these foundational studies fare with respect to the Universal Generalization...
The poset of proper divisibility
2016-01-18
Speaker: Antonio Macchia (CMUC)
Inspired by the definition of the Buchberger graph of a monomial ideal, we study proper divisibility of monomials as a partial order in N^n, from a combinatorial and topological point of view. From this order relation we obtain a new family of posets, that we call posets of proper...
Change of matrix eigenvalues multiplicity associated with perturbation of a diagonal element or deletion of a row and column
2015-12-16
Speaker: Antonio Leal Duarte (CMUC, Univ. Coimbra)
Given an nxn matrix A, an eigenvalue λ of A and an index i (1\le i \le n) we say that i is downer (respectively neutral or Parter), if the multiplicity of λ in the matrix A(i) (obtained from A by deleting row and column i is smaller (resp equal or greater) than the...
A tropical approach to stable spin curves
2015-11-04
Speaker: Ana Margarida Melo (CMUC, Univ. Coimbra)
The moduli space of spin curves of genus $g$ parametrizes pairs consisting of a curve and a square root of the canonical class on the curve. It is therefore endowed with a forgetful map to $M_g$, the moduli space of curves of genus $g$, which has degree $2^{2g}$. There are different modular...
Invariant factors of matrices over general rings
2015-10-14
Speaker: Joao Filipe Queiró (CMUC, Univ. Coimbra)
This talk is a report on recent work with Cristina Caldeira concerning invariant factors of products of matrices over the class of elementary divisor domains. For an nxn matrix over such a ring R, and a pure submodule of R^n, we define a new type of "Rayleigh functional" and use...
Arbitrary triple systems admitting a multiplicative basis
2015-06-18
Speaker: José María Sánchez Delgado (Univ. Cadiz, Spain)
Let T be a triple system of arbitrary dimension, over an arbitrary base field K and in which any identity on the triple product is not supposed. A basis of T is called multiplicative if for any three elements we have that its product is a multiple (coefficient in K) of some element of the...
On Auslander-Reiten sequences for simple modules in the Borel-Schur algebras
2015-06-03
Speaker: Ana Paula Santana (CMUC/Univ. Coimbra)
I will construct Auslander-Reiten sequences for a large class of simple modules over Borel-Schur algebras. Partial information on the structure of the socles of Borel-Schur algebras will also be given.This is joint work with Karin Erdmann and Ivan Yudin....
Eigenvalues, multiplicities and graphs: recent advances and open problems
2015-06-01
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg, USA)
Let G be an undirected graph on n vertices and let S(G) denote the set of all symmetric matrices with graph G and let L(G) denote the set of all multiplicity lists occurring among the matrices in S(G). The diagonal entries of matrices in S(G) are free. There has long been study of this...
Primitive multiple curves: classification, moduli spaces of sheaves, deformations
2015-05-27
Speaker: Jean-Marc Drézet (Institut de mathématiques de Jussieu, France)
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Yred is smooth. These curves have been defined and studied by C. Banica and O. Forster in 1984.In 1995, D. Bayer and D. Eisenbud gave a complete...
Monóides de Ehresmann
2015-04-15
Speaker: Gracinda M.S. Gomes (DM-FCUL e CEMAT-FCUL, Univ. Lisboa)
Na teoria dos monóides inversos a classe dos próprios, ou E-unitários, tem um papel crucial, já que todo o monóide inverso tem uma cobertura própria (que separa idempotentes), um monóide inverso próprio ...
Borel-Schur algebras of finite representation type
2015-04-15
Speaker: Ivan Yudin (CMUC)
In my talk I will explain what is the representation type of a finite dimensional algebra. Then I will describe the Borel-Schur algebras of finite type. This is a joint work with K. Erdmann and A.P. Santana....
A Néron model of the universal jacobian
2015-04-13
Speaker: David Holmes (Univ. Leiden, The Netherlands)
Every non-singular algebraic curve C has a jacobian J, which is an abelian variety. Choosing a point on the curve determines an `abel-jacobi' map from C to J. The same constructions can be made in families: given a family of non-singular curves (together with a section), one obtains a family...
Covers of the projective plane
2015-03-25
Speaker: Eduardo Dias (Univ. Warwick, UK)
The problem of describing the equations of a projective model of an irregular variety is often a difficult one. In this talk we will focus on the case of irregular surfaces. We will describe the construction of the projective model of an Abelian surface with a polarization of type (1,3) via...
Invariant theory and descent via symmetric monoidal categories
2015-03-11
Speaker: Ehud Meir (Univ. Copenhagen, Denmark)
Let C be a symmetric monoidal K-linear category, where K is an algebraically closed field of characteristic zero. Deligne proved that if C satisfies a certain finiteness assumption, then C is necessarily equivalent to the category Rep_K-G, of the finite dimensional rational...
Plactic, hypoplactic, and Sylvester monoids, and other homogeneous monoids
2015-02-25
Speaker: Alan Cain (CMA, Univ. Nova de Lisboa)
In recent work with Gray and Malheiro, I proved that finite-rank plactic monoids (in which Young tableaux form a cross-section) admit finite convergent presentations and are biautomatic. This seminar will survey three themes arising from this work: (1) Using similar techniques with rather...
On Randic spread
2015-02-04
Speaker: Enide Andrade (Univ. Aveiro)
A new spectral graph invariant spr(R), called Randic spread, is defined and investigated. This quantity is equal to the maximal difference between two eigenvalues of the Randic matrix, disregarding the spectral radius. Lower bounds for spr(R) are deduced, some of which depending on the Randi...
Hexagonal projected symmetries
2015-01-28
Speaker: Juliane Oliveira (Univ. Porto)
Three-dimensional symmetries are often observed as 2-dimensional objects. In this seminar we will provide a description of which 3-dimensional lattices may produce 2-dimensional projected pattern with hexagonal symmetries. As an application we compare some projected spatially periodic...
Hypermaps and their classifications
2014-11-19
Speaker: Domenico Antonino Catalano (Univ. Aveiro)
Problems in hypermap theory have applications to many branches of mathematics. This is a consequence of the different interpretations of the notion of a hypermap. A hypermap is-A representation of a hypergraph (Combinatorics);-A triangulation of a compact surface (Topology);-A quotient of an...
Split Lie algebras and relations with weight modules
2014-11-19
Speaker: José M. Sánchez Delgado (Univ. Cádiz, Spain)
We begin by reviewing the main results of the theory of finite dimensional Lie algebras. We continue by considering the class of split Lie algebras of arbitrary dimension. As a generalization, we study the structure of weight modules over< split Lie algebras.We show that under certain...
Connected components of character varieties and Higgs bundles
2014-11-12
Speaker: André G. Oliveira (UTAD)
Given a compact Riemann surface X and a real reductive Lie group G, let R_G=Hom^{red}(\pi_1 X,G)/G be the space of reductive representations of \pi_1 X in G, the so-called G-character variety of X. This is a space with a very rich topological structure, reflecting the topology of both...
Noncrossing partitions in negative CY triangulated categories
2014-11-05
Speaker: Raquel Coelho Guardado Simões (Univ. Lisboa)
A key way to understand triangulated categories is to look at generators. In the context of positive Calabi-Yau (CY) triangulated categories, such as cluster categories, the most interesting generators seem to be cluster-tilting objects. There are some triangulated categories which are...
Combinatorial Brill-Noether theory
2014-10-01
Speaker: Jorge Sentieiro Neves (CMUC / Univ. Coimbra)
The theory of linear systems on graphs is a recent branch of combinatorics owing its fast development to a link with algebraic and tropical geometry. We will review the general theory leading up to the Brill-Noether theorem, whose purely combinatorial proof is an open problem....
Dimension counts for singular rational curves
2014-07-23
Speaker: Ethan Cotterill (Univ. Federal Fluminense, Niterói, Brazil)
Rational curves are essential tools for classifying algebraic varieties. Establishing dimension bounds for families of embedded rational curves that admit singularities of a particular type arises naturally as part of this classification. Singularities, in turn, are classified by their value...
Composition factors of a tensor product of several symmetric powers
2014-07-16
Speaker: Stephen Donkin (Univ. of York, UK)
We consider the problem of determining which irreducible polynomial modules occur as a composition factor of an m-fold tensor product of symmetric powers of the natural module for the general linear group. The case m=1 was analysed by Krop and Sullivan and they obtained (independently) a...
Effective cones of higher codimension cycles on moduli spaces of curves
2014-07-09
Speaker: Izzet Coskun (Univ. of Illinois at Chicago, USA)
I will report on joint work with Dawei Chen where we study effective cones of higher codimension cycles on moduli spaces of curves.We show certain geometrically defined cycles span extremal rays in the effective cone. In particular, we prove that codimension two boundary strata are extremal....
On Butler's conjecture
2014-07-02
Speaker: Leticia Brambila-Paz (CIMAT, Mexico)
D.C. Butler conjectured that the kernel of the evaluation map of a general generatedcoherent system over a general curve is stable. In this talk I will explain theproof of the conjecture for linear series. This is a joint work with Usha Bhosleand Peter Newstead....
The average covering number of a graph
2014-06-23
Speaker: Derya Dogan (Celal Bayar Univ., Turkey)
There are occasions when an average value of a graph parameter gives more useful information than the basic global value. In this talk, we introduce the concept of the average covering number of a graph (the covering number of a graph is the minimum number of vertices in a set with the...
Polar maps, foliations, characteristic classes
2014-06-18
Speaker: Nivaldo Medeiros (Univ. Fluminense, Brazil)
To each hypersurface X in the projective n-space, we associate a rational map Pn--->Pn, called its polar map, given simply by the partial derivatives of the polynomial that defines X. This is a classical theme in projective geometry; the central problem is the classification...
Boundary points of the ELSV compactification
2014-06-11
Speaker: Bashar Dudin (CMUC)
The celebrated ELSV formula relates the number of covers of the projective line having a given profile over one point and fixed branch points to intersection numbers on the the moduli space of stable marked curves. The former number is essentially of combinatorial nature and boils down to...
Gangster operators and invincible positive semi-definite matrices
2014-05-21
Speaker: Charles R. Johnson (The College of William & Mary, USA)
In the relatively new subject of semidefinite programming, positive definiteness plays the role of scalar positivity and inequalities in the PSD partial order replace standard inequalities, relative to linear programming. The subject hashad great success in solving or approximately solving...
Semisimple Hopf algebra actions
2014-05-07
Speaker: Christian Lomp (Univ. Porto)
We review Hopf algebra actions on rings with particular emphasis on a question raised by Miriam Cohen in 1985 whether the smash product A\# H of a semisimple Hopf algebra H acting on a semiprime algebra A is itself a semiprime ring. This question is open until now. In my talk I give a...
Growth and periodicity in representation theory
2014-05-07
Speaker: Karin Erdmann (Univ. Oxford, UK)
We consider finite-dimensional modules of finite-dimensional algebras. Any such module has a (unique) minimal projective resolution, that is, a resolution where terms are direct summands of free modules, as small as possible. One would like to know its rate of growth, known as the...
On Chow stability for algebraic curves
2014-04-09
Speaker: Hugo Torres Lopez (CIMAT, Mexico)
In the last decades there have been introduced different concepts of stability for proyective varieties. In this talk we recall the Chow stability introduced by Mumford for projective varieties, and we prove a natural and intrinsic criterion of the Chow stability for irreducible smooth...
Hermitian matrices and Hodge numbers of irregular algebraic surfaces
2014-04-02
Speaker: Margarida Mendes Lopes (IST/UL)
In this talk it will be explained how properties of spaces of hermitian matrices can be used to obtain lower bounds for the h^1,1 Hodge number of irregular algebraic surfaces and in particular to show the non existence of surfaces with certain invariants. After a brief explanation of the...
Sums of squares on the hypercube
2014-03-05
Speaker: João Gouveia (CMUC/Univ. Coimbra)
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of squares of rational functions modulo the vanishing ideal I(X). We are interested in the existence of rational function representations of small degree. We will show how to derive a general...
Surfaces with p_g=0, K^2=3 and 5-torsion
2014-02-26
Speaker: Carlos Rito (Univ. Porto)
There is (almost) no information available on the literature about complex algebraic surfaces of general type with geometric genus pg=0, self-intersection of the canonical divisor K2=3 and with 5-torsion.If S is a quintic surface in P3 having 15 3-divisible ordinary cusps as only...
Combinatorial Game Theory: a survey
2014-02-05
Speaker: Carlos Pereira dos Santos (ISEC)
In the first years of the 20th century the analysis of the game of nim (by the mathematician Charles L. Bouton) triggered the outburst of a completely new mathematical subject: Combinatorial Game Theory. The aim of this seminar is to give a survey of the development of this mathematical...
2A-replication and the Baby Monster
2014-01-22
Speaker: Rodrigo Farinha Matias (CMUC, Univ. Coimbra)
In the first half of this seminar we will make an introduction to "Moonshine". Namely, we will talk about modular forms, Hecke operators, the Monster Group, Kac-Moody-Lie algebras, vertex algebras, replicability of power series and how these structures are all interrelated to each...
Rainbow connection in graphs
2013-12-04
Speaker: Henry Liu (Univ. Nova de Lisboa)
For a connected graph G, the rainbow connection number rc(G) is the minimum number of colours required to colour the edges of G so that, any two vertices are connected by a "rainbow" path (i.e., using distinct colours). The function rc(G) was introduced by Chartrand, Johns, McKeon...
Supercharacters, non-commuting symmetric functions and set partition combinatorics
2013-11-27
Speaker: Carlos André (Univ. Lisboa)
The representation theory of the symmetric group is a fundamental model in combinatorial representation theory because of its connections to partition and tableaux combinatorics. It has become clear in recent years that the super-representation theory of the finite unitriangular group has a...
Codes over a weighted torus
2013-11-13
Speaker: Jorge Sentieiro Neves (CMUC, Univ. Coimbra)
We will describe a new family of linear codes, extending the notion of projective generalized Reed-Muller codes to a setting where the grading of the polynomial ring is non-standard. We will show how the invariants of the numerical semigroup generated by the weights of the variables come...
Gray codes and lexicographical combinatorial generation for nonnesting and sparse nonnesting set partitions
2013-10-09
Speaker: Alessandro Conflitti (CMUC, Univ. Coimbra)
I shall discuss about combinatorial Gray codes and explicit designs of efficient algorithms for lexicographical combinatorial generation of the sets of nonnesting and sparse nonnesting set partitions of length n and type A....
Some basic spectral properties of complex tridiagonal matrices and the one-dimensional perturbations method.
2013-07-25
Speaker:
Mikhail Tyaglov (Shanghai University, China)
In the talk we give some properties of the spectrum and the root subspaces of an arbitrary complex tridiagonal matrix. We also consider the related sequences of orthogonal polynomials and study their roots. Finally, we discuss some applications of the one-dimensional perturbations method...
Formal deformations and q-deformations in stage, and Hom-algebras
2013-06-12
Speaker: Abdenacer Makhlouf (Univ. de Haute Alsace, France)
In this talk I will provide two point of views for deforming algebraic structures. The first approach is formal deformations introduced by Gerstenhaber for associative algebras, using one parameter formal power series, and then extend to Lie algebras by Nijenhuis and Richardson. It will be...
\(3\times 3\) matrices with a flat portion on the boundary of the numerical range
2013-05-29
Speaker: Fatemeh Esmaeili Taheri (CMUC PhD student)
In recent years, many studies have been done on the numerical range of matrices and bounded operators. In this presentation, the set of unitarily irreducible complex 3×3 matrices whose numerical range has a flat portion will be explicitly described and it will show that this set is connected...
A bijection for the convolution of central binomial coefficients
2013-05-29
Speaker: Rui Duarte (Univ. Aveiro)
All known bijective proofs for the convolution of central binomial coefficients $\sum_{i+j=n} \binom{2i}{i} \binom{2j}{j} = 4^n$,are based, with some variations, on the count of lattice paths. In this talk we give a new proof of this identity, where $\binom{2 \ell}{\ell}$ is regarded as the...
Some semigroup-theoretic aspects of Rauzy graphs of subshifts
2013-05-22
Speaker:
Alfredo Costa (CMUC/Univ. Coimbra)
Symbolic dynamical systems, also called subshifts, correspond in a natural way to factorial prolongable languages. In this context, it is often relevant to study factor graphs, sometimes called Rauzy graphs, to which one gives a natural automaton structure. In this talk we first discuss the...
Classification of quadratic Lie algebras of low dimension
2013-04-30
Speaker: Said Benayadi (Univ. de Lorraine, France)
In this talk we give the classification of the irreducible non solvable Lie algebras of dimension less than or equal to 13 with nondegenerate, symmetric and invariant bilinear forms....
On the structure of graded Leibniz algebras
2013-04-30
Speaker: José M. Sánchez Delgado (Univ. Malaga, Spain)
We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field. We show that any of such algebras with a symmetric G-support is the sum of a subspace of L_1 (the homogeneous component associated to the unit element 1 in G) with a family of I_j, a...
Quaternion arithmetic: factorization and geometry
2013-04-17
Speaker: António Machiavelo (CMUP/Univ. Porto)
The ring of the so called Hurwitz integers, which contains the integral quaternions, being both a left and a right PID, is the appropriate ring inside the quaternions in which to study arithmetical questions. The fact that it is a non commutative ring entails some complications, but also...
On quasi-étale quotients of products of two curves
2013-04-17
Speaker: Roberto Pignatelli (Univ. degli studi di Trento, Italy)
I will consider finite groups acting on the products of two complex algebraic curves freely out of a finite set of points. Geometrically, this means that the map onto the quotient is quasi-étale. I will describe some results obtained in the last few years by several authors including...
Infinitesimally injective polynomial modules
2013-04-03
Speaker: Steve Donkin (Univ. of York, UK)
Working over a field of positive characteristic, we consider the problem of describing, by highest weight, the injective polynomial injective modules for the general linear group GL(n) which are also injective as restricted modules for the general linear Lie algebra gl(n). This is equivalent...
Automatic presentations for algebraic and combinatorial structures
2013-03-20
Speaker: Alan J. Cain (Univ. Porto)
An automatic presentation (also called an FA-presentation) is a description of a relational structures using regular languages. The concept of FA-presentations arose from computer scientists' need to extend finite model theory to infinite structures. Informally, an FA-presentation consists...
Derivatives of functions of matrices
2013-03-06
Speaker: Pedro J. Freitas (Univ. Lisboa)
There have been recent results concerning directional derivatives, of degree higher than one, for the determinant, the permanent, the symmetric and the antisymmetric power maps, by R. Bhatia, P. Grover and T. Jain. We present generalizations of these results for immanants and other symmetric...
A Cauchy kernel expansion and Fomin's growth diagrams.
2013-02-27
Speaker: Aram Emami (CMUC)
We give a bijective proof of a Lascoux's Cauchy kernel expansion over Ferrers shapes, in two families of Demazure operators. The proof is given in the framework of Fomin's growth diagrams for generalized Robinson-Schensted-Knuth correspondences, in our case, to obtain pairs of semi-skyline...
Monochromatic Kr-decompositions of graphs
2013-01-23
Speaker: Teresa Maria Jerónimo Sousa (Univ. Nova de Lisboa)
Given graphs G and H, and a colouring of the edges of G with k colours, a monochromatic H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a monochromatic graph isomorphic to H. Let $\phi_{k}(n,H)$ be the smallest number t, such that...
Schreier graphs of self-similar groups
2012-12-12
Speaker: Daniele D'Angeli (Univ. Trás-os-Montes e Alto Douro)
Self-similar groups are described as groups acting by automorphisms on a rooted tree and have been used to find examples of groups with special and exotic properties. Schreier graphs naturally appear in this context as orbital graphs of the action on the levels of the tree. In this talk I...
Representations and combinatorics related to the Weyl algebra
2012-12-05
Speaker: Samuel Lopes (Univ. Porto)
We consider the multiplication and differentiation operators x and d/dx, which generate the Weyl algebra. Fix a nonzero polynomial h=h(x) and let y be the operator h.d/dx, so that x and y satisfy the commutation relation [y, x]=h. The algebra generated by x and y is denoted by A_h and is a...
Recent developments in matrix pencils completion problems
2012-11-21
Speaker: Marija Dodig (CELC, Univ. Lisboa)
In this talk we shall present some new results on matrix pencil completions. The common point of all of them is a purely combinatorial problem involving triples of partitions. We shall show a solution to the combinatorial problem and give various examples of its applications to matrix...
A meeting point between matroid and representation theory
2012-11-07
Speaker: Inês Legatheaux Martins (CELC, Univ. Lisboa)
In this talk, we introduce a matroid invariant known as the rank partition which was defined by J. A. Dias da Silva in 1990. For matroids realizable over the complex numbers, following recent work of A. Berget, we explain how this concept relates matroid theory to the representation theory...
On a family of log-concave symmetric unimodal polynomials.
2012-10-24
Speaker: José Agapito Ruiz (FC, Univ. Lisboa)
I will show the construction of an interesting family of polynomial sequences out of a suitable expansion of powers of the monomial (xr Ds), where x stands for multiplication by x and D is the usual derivative operator. Two well-known members of this family are the Eulerian polynomials and...
Asymptotic behaviour of a class of regular maps
2012-10-17
Speaker: António João Breda D'azevedo (Univ. Aveiro)
Regular maps are triples $(G,a,b)$ consisting of a group $G$ and a pair $(a,b)$ of generators of $G$ (in fact a conjugacy class) being the product $ab$ an involution. A regular map ${\cal M}=(G,a,b)$ is reflexible or chiral according as $\cal M$ is isomorphic or not to its mirror image...
Even surfaces with genus 4 and bigenus 13
2012-06-27
Speaker: Roberto Pignatelli (Università degli studi di Trento, Italy)
In the study of algebraic surfaces, the surfaces of general type form the biggest and most mysterious class. There is no hope to get a complete classification of them but some interesting results can be obtained by fixing some (topological and birational) invariants: the most important are...
Endomorphism algebras of some modules for Schur algebras and representation dimension
2012-05-16
Speaker: Stephen Donkin (University of York, UK)
This is joint work with H. Geranios. In a recent paper Miemietz and Oppermann show that, for fixed n\geq 2, the representation dimension of the Schur algebra S(n,r) goes to infinity with r, under certain characteristics restrictions. We show that this the result is valid without...
Counting spectral radii of matrices with positive entries
2012-03-21
Speaker: Pedro Freitas (CELC/Mat. FCUL)
We will present some results concerning the number of different spectral radii that you can get for matrices with entries in a prescribed finite set of positive integers. This problem is related to a conjecture by Erdös and Szemerédi about sums and products of elements in a...
On the enumeration of connected graphs with specified biconnected components
2012-03-14
Speaker: Ângela Mestre (CELC)
We derive a recurrence for the number of connected graphs whose biconnected components are all graphs on the same vertex and edge numbers. The proof uses Abel's binomial theorem and generalizes Dziobek's induction proof of Cayley's formula....
Semi-skyline augmented fillings and a non-symmetric Cauchy identity in type A
2012-03-07
Speaker: Aram Emami (PhD student CMUC)
The well known Cauchy identity is the best characterization of Schur functions that can be derived using the Robinson-Schensted-Knuth (RSK) correspondence. The Cauchy kernel expands as a sum, over all partitions, of products of Schur functions in variables X and Y separately. The RSK...
Immanant preserving and immanant converting maps
2012-02-29
Speaker: Maria Antónia Duffner Monteiro (CELC/Mat. FCUL)
Let Mn be the algebra of all n-square complex matrices. I will characterize maps φ:Mn→Mn that satisfy: dχ(φ(A)+λφ(B)) = dχ'(A+λB) for all A,B ∈ Mn and every complex number λ; where χ and χ' are arbitrary irreducible...
Enumerative results and poset structure for a class of binary matrices equipped with a generalization of the Bruhat order
2012-02-22
Speaker: Alessandro Conflitti (CMUC)
Recently, Brualdi et al. defined a partial order on an interesting class of binary matrices which generalizes the classical Bruhat order on the symmetric group, seen as the set of permutation matrices. We study the structure of this poset, and we give some enumerative results, e.g. about the...
Ribbon Schur functions with full support and Schur positivity
2012-02-15
Speaker: Olga Azenhas (CMUC/Univ. Coimbra)
It is known that the Schur expansion of a skew Schur function runs in a subposet of the dominance lattice with top element and bottom element. The support of a skew Schur function consists of the partitions indexing Schur functions which appear in the Schur expansion with a positive...
On the solution set of the matrix equation AX-XA=I
2012-02-01
Speaker: Eduardo Marques de Sá (CMUC)
Matrix equations like AX-YB=C and AX-XB=C have been extensively studied in the literature because of their importance in linear control. The case AX-XA=I has also been considered, though briefly; as the commutator AX-XA has zero trace, our equation has solutions only if the base field has...
Counting dominant regions in the m-extended Catalan arrangement with a fixed separating wall
2012-01-18
Speaker: Eleni Tzanaki (Univ. of Crete, Greece)
Athanasiadis introduced separating walls for a region in the m-extended Catalan arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the m-extended Catalan arrangement for type A and calculate the number of dominant regions which have the fixed...
Compactifications of reductive groups as moduli stacks of bundles
2011-12-14
Speaker: Johan Martens (Aarhus Univ., Denmark)
We will introduce a class of moduli problems for any reductive group G, whose moduli stacks provide us with (toroidal) equivariant compactifications of G. Morally speaking, the objects in the moduli problem could be thought of as stable maps of a twice-punctured sphere into the classifying...
Characteristic free resolutions in Schur algebras
2011-11-23
Speaker: Ana Paula Santana (CMUC/Mat. FCTUC)
Using the Borel-Schur algebra, I construct explicit resolutions of Weyl modules for GL_n and of co-Specht modules. These resolutions provide an answer to the problem, posed in the 80's by A.Akin and D. A. Buchsbaum, of constructing finite explicit and universal resolutions of Weyl modules by...
New approaches to rational curves on general hypersurfaces
2011-11-16
Speaker: Ethan Cotterill (CMUC)
Almost thirty years ago, Herb Clemens made a series of conjectures about rational curves on general projective hypersurfaces, the most famous of which predicts that every rational curve on a general quintic threefold is rigid, in the sense of deformation theory. In this talk we will discuss...
Betti bounds for the Stanley-Reisner ring of a stellar subdivision
2011-11-09
Speaker: Stavros Papadakis (CAMGSD, Lisboa)
The talk will be about recent joint work with Janko Boehm (Saarbruecken) which uses unprojection theory to give bounds for the betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex. ...
Enumeration of Shi regions with a fixed separating wall
2011-11-02
Speaker: Ricardo Mamede (CMUC/Mat. FCTUC)
In 2005 Athanasiadis generalized the Narayana numbers by introducing the concept of separating wall for a region in the extended Shi arrangement. Using this concept, Susanna Fishel, Eleni Tzanaki and Monica Vazirani were able to calculate the number of dominant regions which have a fixed...
Geometric Invariant Theory for polarized curves
2011-10-26
Speaker: Margarida Melo (CMUC/Mat FCTUC)
Geometric Invariant Theory (GIT) was introduced by Mumford and co-authors in order to deal with the problem of constructing quotients of algebraic varieties by the action of an algebraic group. It is particularly useful in the construction of moduli spaces within the category of algebraic...
Tropical Teichmuller theory
2011-10-12
Speaker: Filippo Viviani (CMUC/Roma Tre)
I will report on a joint work in progress with M. Chan and M. Melo in which we study a tropical analogous of the classical Teichmuller theory. In particular, we prove that the moduli space of pure tropical curves (constructed in a joint work with S. Brannetti and M. Melo) is the quotient of...
Positivity, sums of squares and real algebraic varieties
2011-09-28
Speaker: João Gouveia (Mat FCTUC)
In recent years, the theory of sums of squares emerged as a very useful tool for polynomial optimization. The development of approximation methods based on classic Positivstellensatzes, raised a number of interesting theoretical questions that relate to very classic subjects of algebraic...
Sets with small sumset and small periodic product-set
2011-09-14
Speaker: Cristina Caldeira (CMUC/Mat. FCTUC)
We characterize the pairs (A,B) of finite non-empty subsets of a field such that the product-set, AB, is periodic and both the sumset, A+B, and the product-set, AB, are as small as possible, that is, |A+B|=min{p, |A|+|B|-1} and |AB|=max{|A|,|B|}, where p is the characteristic of the...
The subgroup restriction problem for the general linear group
2011-07-20
Speaker: Emmanuel Briand (Univ. Sevilla, Spain)
Let H ⊂ G be reductive groups. Each irreducible representation of G is also a representation of H, but not necessarily irreducible. How does it decompose into irreducibles ? How to describe and compute the multiplicities in its decomposition ? This is the "subgroup restriction...
The degree and the half degree principle for symmetric polynomials
2011-06-15
Speaker: Alexander Kovacec (Mat. FCTUC)
Vlad Timofte proved in 2001/2 that a symmetric real polynomial F of degree d in n variables is nonnegative on certain subsets of Rn if and only if it is so on the subset of points with at most max{|_d/2_|,2} distinct components. His proof used ordinary differential equations. Quite...
A glimpse on vector invariant theory I. The characteristic zero approach (after Capelli and Weyl)
2011-05-27
Speaker: Francesco Regonati (Università di Bologna)
The characteristic zero approach can be founded on the so-called Weyl's Theorem (H. Weyl, The Classical Groups, 1946) which essentially says that a system of generators for the algebra of (absolute) vector invariants for any subgroup G of GL(d) can be constructed by polarizing a system of...
A glimpse on vector invariant theory II. The characteristic free approach (after Rota and De Concini and Procesi)
2011-05-27
Speaker: Andrea Brini (Università di Bologna)
The structure of this talk is the following: -The starting point is the straightening formula for bideterminants (Doubilet, Rota, Stein, 1974) and its analogs for Pfaffians and Gramians (De Concini, Procesi 1976). - From the straightening formulae one derives versions of the E. Pascal...
The singular fibre of the Hitchin map
2011-05-25
Speaker: Peter Gothen (Mat. FCUP / CMUP)
A Hitchin pair on a complex projective curve consists of a vector bundle and an endomorphism of this bundle, twisted by a fixed line bundle L. Thus, when L is the canonical bundle of the curve, a Hitchin pair is a Higgs bundle. There is a Hitchin map from the moduli space of Hitchin pairs to...
Curves on irregular surfaces
2011-05-18
Speaker: Margarida Mendes Lopes (CAMGSD / IST)
The existence of global 1-forms on surfaces of general type imposes constraints on the existence of curves of low genus on the surface. Also sometimes the existence of certain curves on these surfaces allows us to understand or characterize the surface. In this talk I'll discuss some of...
On the birational geometry of the universal Picard variety
2011-04-27
Speaker: Filippo Viviani (CMUC/Univ. Roma 3)
We compute the Kodaira dimension of the universal Picard variety parameterizing line bundles of degree d on curves of genus g under the (technical) assumption that gcd(d-g+1,2g-2)=1. We also give partial results for arbitrary degrees d and we investigate for which degrees the universal...
Hyperplane arrangements: bijections and enumeration
2011-04-13
Speaker: Alessandro Conflitti (CMUC)
We survey some recent combinatorial results about bijections between objects connected with hyperplane arrangements, such as dominant regions and alcoves, and other combinatorial objects such as partitions and tableaux, and we present some enumerative formulae. ...
The generating function of simultaneous s/t-cores
2011-03-30
Speaker: William Keith (CELC, Lisboa)
Previous work on partitions simultaneously s-core and t-core has enumerated such partitions broadly, but missing from the literature is a description of the generating function that would count them. We can produce one, following part of Jaclyn Anderson's original proof of the overall number...
Schur positivity and Littlewood-Richardson coefficient inequalities in the multiplicity-free case
2011-03-23
Speaker: Olga Azenhas (CMUC/Mat FCTUC)
A symmetric function is said to be Schur positive (or nonnegative) if its expansion in the Schur basis has only nonnegative integer coefficients. In the recent years, several problems concerning the Schur positivity of certain differences of Schur function products of the form s_\rho ...
Equivariant degenerations of spherical modules
2011-03-16
Speaker: Stavros Papadakis (CAMGSD, Lisboa)
Given a reductive algebraic group G and an invariant Hilbert function h, Alexeev and Brion have defined a moduli scheme M which parameterizes affine G-schemes X with the property that the coordinate ring of X decomposes, as G-module, according to the function h. The talk will be about joint...
Intersection patterns of convex sets
2011-03-02
Speaker: Martin Tancer (Charles Univ., Czech Republic)
Classical Helly's theorem states that if n>d subsets of d-dimensional Euclidean space are such that each d+1 of them have nonempty intersection then the intersection of all is non empty. This theorem can be seen as a theorem on intersection patterns of convex sets. The question of...
The moment problem for continuous positive semidefinite linear functionals
2011-02-23
Speaker: Salma Kuhlmann (Universität Konstanz, Germany)
Let V be the countable dimensional real polynomial algebra. Let \tau be a locally convex topology on V. Let K be a closed subset of Rn, and let M := M{g1,..., gs} be a finitely generated quadratic module in V. We investigate the following question:When is the cone Psd(K) (of polynomials...
Linear Matrix Inequality (LMI) representation of convex semialgebraic sets
2011-02-23
Speaker: Victor Vinnikov (Ben Gurion University, Israel)
Semidefinite programming (SDP) is a powerful new approach in optimization that has blossomed since the mid 1990s. In a SDP problem, we maximize or minimize a linear functional over a convex set in Rd given by {(x1,...,xd) : A0 + x1 A1 + ... + xd Ad \geq 0}, where A0,A1,...,Ad are real...
Compactified Jacobians of singular curves
2011-02-09
Speaker: Margarida Melo (CMUC/Mat FCTUC)
The Jacobian variety of a smooth curve is an Abelian variety that carries important information about the curve itself. Its properties have been widely studied along the decades, giving rise to a significant amount of beautiful mathematics. However, for singular curves, the situation is more...
Parameterized linear codes and algebraic invariants
2011-02-02
Speaker: Maria Vaz Pinto (CAMGSD/IST)
Let K be a finite field and let X be a subset of a projective space over the field K, which is parameterized by the monomials arising from the s edges of a clutter. If S=K[t_1,.., t_s] and I(X) is the vanishing ideal of X, we describe when I(X) is a complete intersection, and in that case we...
Parabolic Kazhdan-Lusztig R-polynomials for tight quotients of the symmetric groups
2011-01-28
Speaker: Francesco Brenti (Univ. of Roma "Tor Vergata", Italy)
We study the parabolic Kazhdan-Lusztig R-polynomials for the tight quotients of the symmetric groups. More precisely, we obtain explicit combinatorial product formulas for these polynomials. As an application of our results, we derive combinatorial closed product formulas for certain sums...
A combinatorial approach to assess the separability of clusters
2011-01-26
Speaker: Jorge Orestes Cerdeira (Instituto Superior de Agronomia, U. T. Lisboa)
Separability of clusters is an issue that arises in many different areas, and is often used in a rather vague and subjective manner. We introduce a combinatorial notion of interiority to derive a global view on separability of a set of entities. We develop this approach further to evaluate...
Twisted multi-derivations
2011-01-19
Speaker: Christian Lomp (CMUP/Mat. FCUP)
A differential graded algebra on a non-commutative algebra A is interpreted as the space of differential forms on A and is usually referred to as a differential calculus on A. Connections in non-commutative geometry are maps from a module M to M tensored with the space of one-forms that...
Admissible sign patterns for certain classes of matrices
2011-01-12
Speaker: Cláudia Mendes Araújo (Dep. Matemática, Univ. Minho)
In qualitative and combinatorial matrix theory, a methodology based on the use of combinatorial information such as the signs of the elements of a matrix is very often useful in the study of some properties of matrices. A matrix whose entries are chosen from the set {+,-,0} is called a sign...
A classical umbral view of the Riordan group and related Sheffer sequences
2010-11-26
Speaker: José Agapito Ruiz (CELC)
The Riordan group is the set of infinite lower triangular invertible matrices with the group operation given by a matrix multiplication that combines both the usual Cauchy product and the composition of formal power series. It is related to a broad family of polynomial sequences in one...
A class of rigid representations associated to linear PDE
2010-11-17
Speaker: Pedro C. Silva (Instituto Superior de Agronomia, U. T. Lisboa)
The monodromy of the local holomorphic solutions of Gauss's hypergeometric equation defines a linear representation of the fundamental group of the Riemann sphere with 3 points removed. This monodromy is therefore determined by matrices A,B,C verifying the relation ABC=I. Riemann...
On cographic toric face rings
2010-09-29
Speaker: Filippo Viviani (CMUC/Roma Tre)
Toric face rings were introduced by Stanley as a simultaneous generalization of simplicial face rings and toric rings. In this talk, I will report on a joint work in progress with S. Casalaina-Martin and J. L. Kass, in which we study certain toric face rings associated to graphs. The...
On the deformations of N-Koszul algebras
2010-09-22
Speaker: Mariano Suarez-Alvarez (Universidad de Buenos Aires, Argentina)
There are two natural notions of deformation applicable to N-Koszul algebras.First, such an algebra can be presented by generators and relations using homogeneous relators of degree N, and it is natural to consider those algebras which are obtained by changing the relators by adding to them...
A module model for Azenhas' bijection
2010-07-23
Speaker: Itaru Terada (Grad. School of Math. Sci. Univ. of Tokyo, Japan)
In the spirit of Steinberg's description of the Robinson-Schensted correspondence, or van Leeuwen's description of the Schützenberger involution, we give an interpretation of Azenhas' bijection on Littewood-Richardson tableaux as a bijection between the irreducible components of an...
Upper bounds for the energy of digraphs
2010-06-30
Speaker: Elias Rojas (PhD programme U. Coimbra/U. Porto)
Let D be a digraph, its energy is defined as the sum of the absolutes values of the real parts of the eigenvalues of its adjacency matrix A(D). This concept was introduced by J. Rada in 2008 as a generalization of the concept of graph energy introduced by I. Gutman in 1978. The concept of...
Generalized down-up algebras: their symmetries and arithmetic
2010-06-23
Speaker: Samuel Lopes (CMUP/Mat. Pura FCUP)
Generalized down-up algebras were introduced by Cassidy and Shelton (J Alg 2004) as a generalization of down-up algebras, originally defined by Benkart and Roby (J Alg 1998). The latter were motivated by combinatorial operators on a (q, r)-differential poset.Those generalized down-up...
Highly accurate computation of eigenvalues of tridiagonal matrices
2010-05-19
Speaker: Rui Ralha (U. Minho)
We present a method to improve or just guarantee the accuracy of the approximations delivered by any fast method for the eigenvalues of symmetric tridiagonal matrices.The motivation for this approach is two-folded: 1) the fastest state-of-the-art routines in LAPACK do not always deliver...
On the full interval linear expansion of a skew-Schur function
2010-05-05
Speaker: Ricardo Mamede (CMUC/Mat. FCTUC)
A skew-Schur function can be expressed as a sum of Schur functions with non-negative integer multiplicities given by the well-known Littlewood-Richardson coefficients. These coefficients also govern the decomposition of a product of two Schur functions as a sum of Schur functions....
Connected subgraphs in multicoloured graphs
2010-04-28
Speaker: Henry Liu (FCT-CMA/FCTUNL)
In graph theory, a well-known observation of Erdős and Rado which is often considered as folklore; in fact it is also the first exercise in Béla Bollobás' book "Modern Graph Theory", is the following: For any graph, either it is connected, or its complement...
Quantum integrability and combinatorics: alternating sign matrices, plane partitions and completely packed loops
2010-04-21
Speaker: Tiago Dinis (Université Pierre et Marie Curie)
1, 2, 7, 42, 429, 7436...This sequence appeared for the first time in the study of Alternating Sign Matrices at the beginning of the 80'. With time, mathematicians and physicists got used to seeing this mysterious sequence appear counting sets apparently so different.In this talk I will...
Supercharacter theories, root systems and set partitions
2010-04-14
Speaker: Carlos André (CELC/Mat. FCUL)
In this talk, we survey the basics of supercharacter theories of finite groups with particular emphasis on the finite classical groups of Lie type. We will discuss some (mysterious) connections with the combinatorics of the underlying root system, and show how some supercharacter-theoretic...
Noncrossing and nonnesting partitions of classical Weyl groups
2010-04-07
Speaker: Alessandro Conflitti (CMUC)
We study noncrossing and nonnesting partitions of classical Weyl groups, and we describe bijections preserving openers, closers and transients, between these two kinds of combinatorial structures, with some special emphasis on Coxeter systems of type $D$. This is a joint project with Ricardo...
Stability and moduli spaces of syzygy bundles
2010-03-24
Speaker: Pedro Macias Marques (U. Évora)
It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle E_{d_1,...,d_n} on P^N defined as the kernel of a general epimorphism \phi: O(-d_1)\oplus\cdots\oplus O(-d_n) -> O is (semi)stable. In this talk, attention is restricted to the case of...
Realizing modules over the homology of a DGA
2010-03-10
Speaker: Gustavo Granja (CAMGSD/IST)
Let A be a DGA over a field. A graded module X over H_*(A) is said to be realizable if there exists a DG module M over A with H_*(M)\cong X. There are at least two approaches to finding out whether a module is realizable. One uses Postnikov systems (certain diagrams in the derived category...
A homological hammer to pound an infinite problem into a finite calculation
2010-03-10
Speaker: Thomas Cassidy (Bucknell University, USA)
A list of generators and relations offers a succinct presentation for an algebra over a field, but what can we deduce when looking at this presentation? If two algebras have similar presentations, they may also share other characteristics. I will illustrate several ways in which...
Partial colorings, posets and chromatic polynomials
2010-03-03
Speaker: Domingos Cardoso (U. Aveiro)
Each partial coloring of a vertex subset W of a graph of order n defines a poset whose elements are minors. These minors are obtained by the contraction of edges such that the end-vertices have the same color from an arbitrary vertex coloring of the complement of W. In each of these posets,...
Hook partitions and coding theory
2010-02-24
Speaker: Maria Manuel Torres (CELC/Mat. FCUL)
I will speak about a curious connection between multilinear algebra and coding theory, which was obtained while studying the structure of critical orbital sets associated to hook partitions - this is a joint work with Pedro Cristiano Silva (ISA-UTL)....
Jets of foliations
2010-02-08
Speaker: Eduardo Esteves (IMPA-Brasil)
We will show how to associate sheaves of jets to singular foliations of algebraic varieties, and discuss some of their applications....
Projectively normal embeddings of curves with general moduli
2010-02-08
Speaker: Claudio Fontanari (Università Degli Studi Di Trento, Italy)
In this talk I am going to present a joint work with Edoardo Ballico motivated by a stimulating conjecture due to Aprodu and Farkas. Our main contribution is a suitable improvement in the case of general curves of the classical theorem by Green and Lazarsfeld on the projective normality of...
The ratio field of values, properties and related objects
2010-01-20
Speaker: Charles R. Johnson (College of William and Mary, USA)
A variation on the classical field of values recently arose in numerical analysis. Instead of one matrix, it is a function of two, in which each set element is a ratio of Hermitian quadratic forms at the same vector, as the vectors run over the unit sphere. In the denominator is a matrix...
Unprojection and Stanley--Reisner rings associated to cyclic polytopes
2009-12-16
Speaker: Stavros Papadakis (CAMGSD/IST)
The talk will be about joint work in progress with Janko Boehm (Saarbruecken) concerning the structure of Stanley--Reisner rings associated to cyclic polytopes. In more detail, denote by \Delta C_d(m) the boundary simplicial complex of the d-dimensional cyclic polytope which has m vertices....
Diagonal minus tail forms and Lasserre's sufficient conditions for sums of squares
2009-11-25
Speaker: Carla Fidalgo (ISEC)
By a "diagonal minus tail" form (of even degree) we understand a real homogeneous polynomialF(x_1,...,x_n)=F(X)=D(X)-T(X), where the diagonal part D(X) is a sum of terms of the form b_i x_i^{2d}with all b_i\geq 0 and the tail T(X) a sum of terms a_{i_1i_2...i_n}x_1^{i_1}......
Matrices, RSK correspondence and Kronecker products
2009-11-18
Speaker: Ernesto Vallejo (Instituto de Matemáticas, UNAM)
In this talk we present an extension of the RSK and the dual RSK correspondence to 3-dimensional matrices. We apply this correspondence to obtain an algorithm that permits to compute, out a list of certain matrices, called minimal, several Kronecker coefficients for irreducible characters of...
Combinatorial aspects of Escher Tilings
2009-11-18
Speaker: Srečko Brlek (LACIM/Universitè du Quèbec à Montrèal)
When Maurits Cornelis Escher started to produce astonishing tesselations of the plane in the late 30's, very few properties were known about theses. The ``simplest" tessellations make use of just one polygon or tile for tiling the entire plane, and the polygons that tile the plane by...
On the complexity group of stable curves
2009-10-28
Speaker: Margarida Melo (CMUC/Mat. FCTUC)
In 1969 Deligne and Mumford constructed a remarkable modular compactification of the moduli space of smooth curves of given genus, whose points parametrize stable curves. The geometry of this moduli space is very rich and its study has motivated the development of several important branches...
Linear/Affine dependencies of (0,1) vectors
2009-10-14
Speaker: Ilda Perez Silva (CELC/Mat. FCUL)
I will present and discuss recent results and conjectures concerning the following open problem: Is it possible to define the affine dependencies over the reals of the set Cn:={0,1}n in a purely combinatorial way, i.e. without any reference to the field R? More precisely, I will sketch the...
Constructions of bipartite hypermaps
2009-10-07
Speaker: Rui Duarte (Univ. Aveiro)
A hypermap is a cellular imbedding of a hypergraph on a surface. A hypermap is bipartite if we can divide its set of hypervertices in two parts in such a way that consecutive hypervertices around a hyperedge or a hyperface are contained in alternate parts. In this talk we will see some...
On the tropical Torelli map
2009-09-30
Speaker: Filippo Viviani (CMUC/Roma Tre)
The classical Torelli map is the modular map from the moduli space of curves of genus g to the moduli space of principally polarized abelian varieties of dimension g, sending a curve into its Jacobian. The Torelli map is known to be injective (Torelli theorem) and the image has been...
Chirality under a combinatorial point of view
2009-07-15
Speaker: António João Breda (Univ. Aveiro)
Although the phenomenon of chirality appears in many areas of science, specially in chemistry, in mathematics it appears essentially in topological, geometrical and combinatorial forms. Chirality in maps and hypermaps (combinatorial and algebraic form of chirality) is not merely a binary...
Fourier-Mukai transforms and moduli spaces of semistable sheaves for genus 1 curves
2009-07-07
Speaker: Ana Cristina López Martín (Univ. Salamanca, Spain)
Since its introduction, the Fourier-Mukai transform has been a very important tool for the study of the properties of moduli spaces of sheaves and vector bundles. For instance, Atiyah's characterization of vector bundles allowed Tu to give a geometric description of the moduli spaces of...
Restricted involutions and Motzkin paths
2009-06-16
Speaker: Marilena Barnabei (Univ. Bologna, Italy)
We show how a bijection due to Biane between involutions and labelled Motzkin paths yields bijections between Motzkin paths and two families of restricted involutions that are counted by Motzkin numbers, namely, involutions avoiding 4321 and 3412. As a consequence, we derive...
Compact complex surfaces of genus 0
2009-06-09
Speaker: Roberto Pignatelli (Università degli Studi di Trento, Italy)
There is only one compact complex curve of genus 0, the Riemann sphere. In the XIX century M. Noether conjectured a similar statement in dimension 2: is every compact complex surface without nonzero holomorphic differential forms a rational surface? The first counterexample to this...
Schur algebras
2009-05-26
Speaker: Ana Paula Santana (CMUC/Mat. FCTUC)
In the first part of the talk I introduce Schur algebras. The second part will focus on recent developments on the construction of minimal projective resolutions of Weyl modules for the Schur algebra for GL(n)....
Properties of Dawson's distance in a power set
2009-05-12
Speaker: António Guedes de Oliveira (Univ. Porto)
(Joint work with D. Oliveira e Silva, J. Brunat and M. Noy.)Given a matroid over E={1,2,...,n}, consider for each basis B the sets that contain B*, the set of elements of B that are (relatively to B) not internally active, and that are contained in B', the union of B with the set of the...
Whitney numbers of order ideals for some interesting classes of posets
2009-04-28
Speaker: Alessandro Conflitti (CMUC)
...
Tableaux, puzzles and mosaics: Reduction of the conjugation symmetry of Littlewood-Richardson coefficients to the Schützenberger involution
2009-03-31
Speaker: Olga Azenhas (CMUC/Mat. FCTUC)
...
Geometry and complexity of partition bijections
2009-03-20
Speaker: Igor Pak (School of Mathematics, University of Minnesota)
The study of partition identities has a long history going back to Euler, with applications ranging from Analysis to Number Theory, from Enumerative Combinatorics to Probability. Partition bijections is a combinatorial approach which often gives the shortest and the most elegant proofs of...
A Postscript to Serre
2009-03-03
Speaker: Fernando Q. Gouvêa
(Colby College, Maine, EUA)
Now that Serre's modularity conjecture has been proved by Khare and Wintenberger, one can show, using a method due to Serre himself, that the Galois representation associated to the middle cohomology of a rigid Calabi-Yau threefold defined over Q comes from a modular form. We will explain...
Introduction to Coxeter Groups
2009-02-10
Speaker: Ricardo Mamede (CMUC/Mat. FCTUC)
This seminar is an introduction to the theory of Coxeter groups and
their geometric representations as groups of transformations of real
vector spaces.
Area(s): ...
A bijection between noncrossing and nonnesting partitions of types
A and B
2009-02-10
Speaker: Ricardo Mamede (CMUC/Mat. FCTUC)
The total number of noncrossing partitions of type $\Psi$ is the $n$th
Catalan number $\frac{1}{n+1}\binom{2n}{n}$ when $\Psi=A_{n-1}$,
and the binomial $\binom{2n}{n}$ when $\Psi=B_n$, and these numbers
coincide with the correspondent number of nonnesting partitions. For
type A,...
Steiner bundles on algebraic varieties
2009-01-20
Speaker: Helena Soares (ISCTE)
(joint work with Rosa Maria Miró-Roig)
Steiner bundles on projective spaces were first defined by Dolgachev and
Kapranov as vector bundles E on P^n fitting in an exact sequence of the form
0 -- /O/(-1)^s -- /O/^t -- E -- 0.
Steiner bundles have rank t-s= n and it is well...
Patterns of commutativity and Bilinear Systems of Equations
2009-01-20
Speaker: Charles R. Johnson (College of William and Mary, USA)
Given a pair of n-by-n zero/nonzero patterns for two matrices,
how can we tell when they admit a commuting pair. A number of
interesting questions are of this form, and thoughts about it lead to
many interesting questions. Like other qualitative matrix theoretic
questions, this...
Parallel Kustin-Miller Unprojection
2009-01-13
Speaker: Jorge Neves (CMUC/Mat. FCTUC)
Given a Gorenstein graded ring R and an ideal
I of codimension 1, such that R/I is also Gorenstein,
one can define a new graded ring, R_un, as the quotient of
R[y] by an ideal J, obtained from I.
This new graded ring is called
the Kustin-Miller unprojection of R,I. Geometrically, this...
Extensions of Positive Definite Functions on Groups
2008-12-16
Speaker: Mihály Bakonyi (CELC)
In the beginning, generalities about the theory of positive definite extensions
of partially definite matrices are presented. Undirected graphs are associated
with such matrices, and the importance of chordal graphs in this context is underlined. The results are later used for proving...
Computing the Conditioning of the Components of a Linear Least Squares Solution
2008-12-02
Speaker: Marc Baboulin (CMUC/Mat. FCTUC)
We address the accuracy of the results for the overdetermined
full rank linear least squares problem. We recall theoretical results
on conditioning of the least squares solution and the
components of the solution.
Then we define computable estimates for these condition numbers and we...
Unprojection and stellar subdivisions of simplicial complexes
2008-10-14
Speaker: Stavros Papadakis (CAMGSD/IST)
Unprojection theory aims to construct and analyze commutative rings
in terms of simpler ones. The talk will be about joint work
in progress with Christos Athanasiadis (Athens) and Janko Boehm
(Saarbruecken) that relates, on the algebraic level of
Stanley-- Reisner rings, stellar...
Littlewood-Richardson coefficients, the hive model and Horn inequalities
2008-09-19
Speaker: Ron King (University of Southampton)
Littlewood-Richardson (LR) coefficients arise as integer multiplicities
in the decomposition of products of Schur functions. The hive model is introduced
as a means of evaluating these coefficients combinatorially. By using edge rather
than vertex labelling of LR-hives it is shown that...
Growth diagrams, and increasing and decreasing chains in fillings of
cell diagrams
2008-09-19
Speaker: Christian Krattenthaler (Wien UniversitÀt)
Recently, there has been a series on articles on the number of fillings of cell diagrams with restrictions on their increasing and decreasing chains, most notably the paper by Chen, Deng, Du, Stanley and Yan on matchings and set partitions with restrictions on their "crossings" and...
Skew product of rings over a monoid
2008-07-01
Speaker: Ivan Yudin (CMUC)
Let G be a monoid, A a G-graded algebra and B a G-algebra.
We define a new algebra $A\ltimes_G B$ called the skew product of A
on B over G.
We will discuss homological properties of quotient algebras of
$A\ltimes_G B$.
Area(s): ...
A variation on the tableau-switching and a Pak-Vallejo' conjecture
2008-06-11
Speaker: Olga Azenhas (CMUC/Mat. FCTUC)
Four Young tableau bijections exhibiting the commutativity symmetry of
the Littlewood-Richardson coefficients are known. Pak and Vallejo
conjectured (2004) that, despite the different operations defining
them, they are identical in the sense that they produce the same
outcome. It...
Minimum Decompositions of Graphs
2008-05-28
Speaker: Teresa Sousa (CMA/Mat. FCTUNL)
Given graphs G and H, an H-decomposition of G is a partition of the edge set of
G such that each part is either a single edge or forms a graph isomorphic to H.
Let \phi_H(n) be the smallest number, \phi, such that any graph G of order n admits an
H-decomposition with at most \phi...
Representation of integers by linear forms
2008-05-20
Speaker: Manuel Silva (CMA/Mat. FCTUNL)
Let A be a set of positive integers and f(x,y) a polynomial
with integer coefficients. For every integer n, let r_{f,A}(n)
denote the number of representations of n in the form n =
f(a1,a2) where a1 and a2 belong to A. We will discuss several recent
problems dealing with the case when...
Schensted correspondence and Littelmann paths.
2008-04-08
Speaker: Karin Erdmann (University of Oxford)
This is on joint work with J.A. Green and M. Schocker. The aim is to
explain the Littelmann path model for $gl_n$. In this case, Littelmann's
'paths' become 'words'. This leads to the representation theory of the
'Littelmann algebra' which is a close analog of the Schur algebra.
...
A geometric description of m-cluster categories
2008-03-17
Speaker: Robert Marsh (University of Leeds)
[Joint work with Karin Baur (ETH, Zurich).]
Cluster categories are categories arising in the representation theory
of algebras as categorical models of Fomin-Zelevinsky cluster
algebras, which were introduced to study the multiplicative properties
of the dual canonical basis of a...
Cluster Algebras
2008-03-12
Speaker: Raquel Simões (CAUL)
Cluster algebras were introduced by Fomin and Zelevinsky in 2001, in order to study the dual canonical basis of a quantum group. The theory of cluster algebras has many connections and applications in many different areas, namely the representation theory of algebras.
In this seminar it...
Sparsity Analysis of QR factorization
2008-03-04
Speaker: Charles Johnson (College of William and Mary)
For many years it was known that the factors Q and R in the QR factorization of a sparse matrix A might necessarily be sparser than conventional analysis predicted. We show why and give a precise prediction of the sparsity. It is a nice application of algebraic ideas associated with...
Eigenvalues of matrices with a given graph
2007-12-12
Speaker: António Leal Duarte (CMUC/Mat. FCTUC)
Given a graph G on n vertices the generalized
inverse eigenvalue problem for G consists in
describing the all the possible sequences of
2n-1 real numbers such that there exists a real
matrix symmetric matrix A whose graph is G, whose
eigenvalues are the first n elements of the...
The Hankel Pencil Conjecture
2007-11-28
Speaker: Alexander Kovacec (CMUC/Mat. FCTUC)
In 1968 Heyman proved a lemma that turned out to be a corner stone for the
theory of linear multivariable state space systems, a branch of control
theory: he showed that fields have the feedback cyclization- or FC-property,
that is,
every reachable pair $(A,B)$ of matrices over the...
Construction of a surface of general type with p_g=q=1 and K^2=6
2007-10-24
Speaker: Carlos Rito (Mat. UTAD)
Complex algebraic surfaces of general type with p_g=q=1 are not yet completely understood. Until recently
only a few examples were known. In this talk I will use the Computational Algebra System Magma to construct such
a surface with K^2=6, as a double cover of a Kummer surface (quartic...
Posets, Boolean Algebras, and Spectrum
2007-10-17
Speaker: Alessandro Conflitti (CMUC)
We discuss some properties related with the spectrum of the undirected
Hasse diagram of finite posets, with special emphasis on Boolean Algebras. Area(s): ...
Akivis superalgebras
2007-10-03
Speaker: Ana Paula Santana (CMUC/Mat. FCTUC)
In this talk I define Akivis superalgebras and study enveloping
superalgebras for this class of algebras, proving an analogous of the
PBW Theorem.
Lie and Malcev superalgebras are examples of Akivis superalgebras.
The connection between the classical enveloping superalgebras and...
Projective resolutions in Schur algebras
2007-07-24
Speaker: Ivan Yudin (CMUC)
The Schur algebras play an important role in the representation
theory of general linear and symmetric groups. In this talk we
discuss a construction of projective resolutions of modules over
Schur algebras. Area(s): ...
A new Gorenstein format
2007-07-10
Speaker: Jorge Neves (CMUC/Mat. FCTUC)
The construction of projective varieties in Algebraic Geometry using graded rings is hindered by the absence of general structure theorems for homogeneous ideals in codimension \geq 4. In this talk we explain some new results obtained by joint work with Papadakis. We describe a new format of...
Mumford's stability on the Sato Grassmannian
2007-06-26
Speaker: Ana Casimiro (Mat. FCTUNL)
We give a notion of stability on the infinite Grassmannian
Gr(k((z))^{\oplus r}) for the action of the group Sl(r,k[[z]]) coherent with
the classic stability notion for vector bundles over a curve. We give a
numerical criterium and prove the existence of some geometric quotients....
Identical involutions on pairs of tableaux
2007-04-17
Speaker: Olga Azenhas (CMUC/Mat. FCTUC)
Schur functions constitute a distinguished basis for the ring
of the symmetric functions. The rule of Littlewood-Richardson
gives the decomposition of a product of two Schur functions
in the basis of the same functions and the coefficients are the
so called Littlewood-Richardson...
Semigroups of Transformations and the classification of finite
simple groups
2007-02-27
Speaker: João Araújo (CAUL/Mat. U. Aberta)
In this talk we are going to show how the classification of
finite simple groups has been used to solve some longstanding open
problems in the theory of semigroups.
Area(s): ...
On noncommutative hypergeometric series
2007-02-13
Speaker: Alessandro Conflitti (CMUC)
We provide two different noncommutative versions of the Gauss
hypergeometric function, in the most general setting of hypergeometric
functions over an abstract unital Banach algebra, and we show that any of
them is the unique solution of a differential hypergeometric equation...
Simultaneous conjugation of 2 by 2 matrices and geometric invariant theory
2007-01-30
Speaker: Carlos Florentino (CAMGSD/Mat. IST)
We present the general problem of constructing geometric
quotients and orbit spaces. The study of simultaneous
conjugation of several complex m by m matrices can be viewed
as a particular instance of this problem, and in this case
the generic orbits have well-known descriptions.
...
Copositive Matrices: A Survey
2007-01-23
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg,USA)
A real n-by-n matrix A is said to be copositive if x^TAx = 0 whenever x
is an entry-wise nonnegative vector. Despite the simple definition, the
class is both important and very subtle to analyze. We will survey the
simple properties of copositive matrices, then some of the history...
Hall's Universal Group
2007-01-11
Speaker: Stephen Donkin (University of York)
We see what happens to the representation theory of a finite
group "in the limit", i.e. as the group gets arbitrarily large.
Technically, this is done via Hall's Universal Group U. This is a group
which contains a copy of every finite group in such a way that isomorphic
finite...
The BSSV-conjecture
2006-11-28
Speaker: Wiland Schmale (University Carl v. Ossietsky, Germany)
A conjecture by Bumby, Sontag, Sussmann and Vasconcelos from 1981 says:
A weakend form of the classical "Heymann's Lemma" from Control Theory is valid also for reachable linear sytems over complex polynomials.
In my talk Heymann's Lemma, the BSSV-conjecture and related results so...
The independent resolving number of a
graph
2006-10-31
Speaker: Varaporn Saenpholphat (Srinahkarinwirot Univ, Thailand)
For an ordered set W{w_1,w_2,...,w_k} of vertices in a connected graph G and a vertex v of G, the code with respect to W is the k-vector
c_W(v)=(d(v,w_1),d(v,w_2),..., d(v,w_k)).
The set W is an independent resolving set for G if W is independent in G and distinct vertices have distinct...
The size of Bruhat intervals between nested involutions in $S_{n}$
2006-09-26
Speaker: Alessandro Conflitti (CMUC)
We build a chain $$\operatorname{id}=\vartheta_{0} Area(s): ...
Gelfand-Tsetlin patterns commute with boundary: a commutativity involution
2006-07-11
Speaker: Olga Azenhas (CMUC/Mat. FCTUC)
Schur functions constitute a distinguished basis for the ring of the symmetric functions. The rule of Littlewood-Richardson gives the decomposition of a product of two Schur functions in the basis of the same functions and the coefficients are the so called Littlewood-Richardson...
Keys, frank words and matrix realizations of pairs of tableaux
2006-06-20
Speaker: Ricardo Mamede (CMUC / Matemática FCTUC)
In this talk, we consider the problem of the existence of a matrix
realization, over a local principal ideal domain, for a pair
$(T,K(\sigma))$, where $T$ is a skew tableau over the alphabet
$\{1,\ldots,t\}$ and $K(\sigma)$ is the key associated with the
permutation $\sigma\in S_t$ with...
Supercharacters, Gelfand pairs and spherical functions
2006-05-16
Speaker: Carlos André (CELC, U. Lisboa)
Supercharacters (and superclasses) were introduced in the 90's for the
unitriangular group over a finite field as an attempt to parameterize the
irreducible characters (and the conjugacy classes). More recently, the theory
has been extended for groups associated with the Jacobson radical...
Maximal surface group representations in isometry groups of classical Hermitian
symmetric spaces
2006-05-02
Speaker: Peter Gothen (CMUP, U. Porto)
Let G be a Lie group. The moduli space of representations of a
finitely generated group in G is by definition the set of homomorphims of the
finitely generated group to G, considered up to overall conjugation by G. Of
particular interest is the case when the finitely generated group is...
Positive, Path-Product and Inverse M-matrices
2006-04-27
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg,USA)
An n-by-n, entry-wise nonnegative matrix is called an inverse
M-matrix (IM) if it is invertible and its inverse has nonpositive
off-diagonal entries. An irreducible IM amtrix is necessarily entry-wise
positive. Both M-matrices and IM matrices arise in a wide
array of applications,...
Polyhedral Complexes, Non-Archimedean Amoebas and Tropical Varieties:
A First Glimpse on Tropical Geometry
2006-04-11
Speaker: João Gouveia (CMUC, U. Coimbra)
Tropical geometry has been around for some time, with different names and in
different contexts. In the last few years, a growing interest appeared on this
subject, motivated by important applications of this theory to Algebraic
Geometry: Tropical Geometry seems to be a strong tool on...
Generalized condition numbers and a problem on absolute norms
2006-03-28
Speaker: João Queiró (CMUC, U. Coimbra)
The condition number of a square matrix measures the sensitivity of the solution
of a system of linear equations with that matrix - or of the inverse of the
matrix -
with respect to perturbations in the data. The ordinary condition number is
defined in terms of the spectral norm. Here we...
Small invariants and big fundamental group
2006-03-14
Speaker: Margarida Mendes Lopes (CAM, IST)
In this talk I wish to present some recent results about the algebraic fundamental group of surfaces of general type with small invariants. After giving a brief introduction to the notion of algebraic fundamental group I will explain some of the techniques behind these results and present...
A categoria de Bernstein-Gelfand-Gelfand
2006-02-21
Speaker: André V. Fonseca
(CAUL, U. Lusófona)
Na teoria de representações de Álgebras de Lie semisimples, a categoria de
Bernstein-Gelfand-Gelfand ocupa um lugar central. Por um lado contém todas
as representações "interessantes" (representações de dimensão finita, módulos
de Verma, módulos simples, etc) e por outro lado está...
Completion of Matrices and Matrix
Pencils
2006-01-17
Speaker: Marija Dodig
(CELC/Univ. de Lisboa)
In this talk, we will give a retrospective of, in our
opinion, the most important results of completion of matrices and
matrix pencils. Also, we will present some generalizations of these
results that we have obtained recently. Specifically, we will show the
result of the general row...
Graphs with regularity constraints
2006-01-10
Speaker: Paula Rama
(Universidade de Aveiro)
Graphs with (k,)-regular sets or equitable partitions are examples of graphs with regularity constraints. In this talk some relations between the existence of such structures in a graph and the properties of the spectrum of the (0,1)-adjacency matrix of the graph and of its line...
How to restore the tuple of matrices by their joint numerical range
2005-12-20
Speaker: Ilya Spitkovsky
(College of William and Mary, USA)
Area(s): ...
Burch's inequality for modules
2005-12-13
Speaker: Ana Luísa Correia
(CELC/Univ. Aberta)
The Rees algebras of ideals were introduced by Rees (1956) to
prove the Artin-Rees' lemma about filtrations of modules. In the 90's,
several mathematicians studied the Rees algebras of modules in order to
generalize for modules some known results for ideals. In this direction,...
Super-characters of finite algebra groups
2005-12-06
Speaker: Alejandro Piñera
(Univ. de Oviedo)
Let $\mathbb{F}_q$ be the finite field of $q$ elements and let $A$
be an associative algebra of finite dimension over $\mathbb{F}_q$.
If the Jacobson radical is $J = J(A)$, then the set $G = 1+J$ is a
subgroup of the units of $A$ called algebra group.
\par In this work we construct the...
A combinatorial Lie idempotent for the symmetric group algebra
2005-11-29
Speaker: Peter McNamara
(IST)
Because they play a role in our understanding of the symmetric group algebra, Lie idempotents have received considerable attention. The Klyachko idempotent has attracted interest from combinatorialists, partly because its definition involves the major index of permutations.
For the...
The congruent number problem. An introduction to number theory
2005-11-29
Speaker: Ariel Pacetti (Univ. de Buenos Aires)
Area(s): ...
Uma conjectura acerca do $\mu$-permanente
2005-11-22
Speaker: Carlos Fonseca
(CMUC, U. Coimbra)
Dados uma matriz quadrada de ordem $n$, $A=(a_{ij})$, e um número
real $\mu$, definimos o $\mu$-permanente de $A$ como sendo o
polinómio
$$P_\mu(A)=\sum_{\sigma\in S_n} a_{1\sigma(1)}\cdots
a_{n\sigma(n)}\,\mu^{\ell(\sigma)}\; ,$$ onde $\ell(\sigma)$ é o
número de inversões da...
Super-Caracteres nos p-subgrupos de Sylow dos grupos simplético e ortogonal
2005-11-08
Speaker: Ana Neto
(Univ. Técnica de Lisboa)
A teoria dos super-caracteres foi desenvolvida por Carlos André para o grupo unitriangular $U_n(q)$ sobre o corpo finito com $q$ elementos e posteriormente estudada por Ning Yan através de uma abordagem diferente.
Seguiremos o trabalho de ambos para estender a noção de...
Pick matrices and comparative stability
2005-11-02
Speaker: Nir Cohen
(UNICAMP, Brasil)
Complex interpolation (Nevanlinna-Pick or
Schur-Caratheodory type) can be explained from several
points of view, and I will offer yet another one:
comparative stability. Here, given two (complex or
real) matrices A,B, the question is to verify whether
every Lyapunov factor for A is a...
Anulamento de Tensores Simétricos decomponíveis
2005-10-25
Speaker: Carlos Gamas
(CMUC, U. Coimbra)
Seja S_{m + n} o grupo simétrico de ordem m+n. Sejam \lambda e \chi caracteres irredutíveis de S_{m +n} e S_{m} respectivamente. Supondo d = (\lambda, \chi)_{S_{m}} \neq 0, define-se a função esférica \phi : S_{m+n} - R pondo
\phi(g) = \frac{\chi (id)}{dm!} \sum_{h \in S_{m}} \lambda(g...
Corners of certain determinantal ranges
2005-06-14
Speaker: Alexander Kova\vcec
(Universidade de Coimbra)
Let $A$ be a complex $n\times n$ matrix and let $\SO(n)$ be the
group of real orthogonal of matrices of determinannt one. Define
$\Delta (A)=\{\det(A\comp Q): Q\in \SO(n)\},$ where $\comp$ denotes the
Hadamard product of matrices. For a permutation $\sigma$ on $\{1,\ldots,n\}$...
Palavras francas e pares de tableaux com realização matricial
2005-06-07
Speaker: Ricardo Mamede
(CMUC, Universidade de Coimbra)
Sejam $\sigma\in S_t$, $t\geq 1$, e $K(\sigma)$ uma chave associada.
Uma chave da permutação $\sigma$, considerada como palavra no
alfabeto $\{1,\ldots,t\}$, é um tableau com colunas comparáveis para
a inclusão, obtido tomando uma sequência de factores à esquerda de
$\sigma$, ordenados...
Problemas de completamento em várias classes de matrizes
2005-05-31
Speaker: Cláudia Araújo
(Universidade do Minho)
Os objectos centrais deste estudo são as matrices parciais. Um conceito simples: matrizes
em que algumas das entradas são especificadas, isto é, elementos conhecidos de um dado conjunto, e as
restantes não são prescritas, sendo tratadas como variáveis livres, usualmente sobre o mesmo...
An introduction to the theory of graph spectra
2005-05-17
Speaker: Drago? Cvetkovic'
(Faculty of Electrical Engineering, Belgrade, Serbia and Montenegro)
The spectrum of a graph is defined as the spectrum of a matrix
associated to the graph; in most cases it is the adjacency matrix
although some other graph matrices are used. The beginnings of the
theory of graph spectra are connected with the first mathematical
paper in the subject,...
Uma acção do grupo simétrico em quadros de Young
2005-04-26
Speaker: Olga Azenhas
(CMUC, Universidade de Coimbra)
?? apresentada uma construção que estende uma acção do grupo simétrico em quadros de Young, definida por A. Lascoux e M. P. Schutzenberger,
em "Keys and standard bases", usando o "jeu de taquin".
Resumidamente a acção a apresentar pode ser vista como uma variação do "jeu de taquin". No...
Tensores decomponíveis imanentais: O problema da igualdade.
2005-04-19
Speaker: Henrique Cruz
(CELC, Universidade da Beira Interior)
Neste seminário vamos apresentar uma condição necessária e
suficiente para a igualdade de dois tensores simetrizados decomponíveis
não nulos, quando o simetrizador está associado a um carácter irredutível
do grupo simétrico de grau m.
Area(s): ...
Integer Matrices and Counting Functions
of Groups
2005-03-22
Speaker:
Gautami Bhowmik,
(Universite de Lille 1,
France)
We will discuss some counting functions of classical groups
and their relationship with integer matrices. These will include some
known functions on GL_n(Z) and some new ones on orthogonal and symplectic
similitudes.
Area(s): ...
Polónia: Independência ou York!
2005-02-22
Speaker: João Araújo
(Universidade Aberta)
Ao longo dos anos 50 e 60 do século passado alguns matemáticos polacos
dedicaram-se a estudar noções de independência, válidas em álgebras
universais, e que continham como casos particulares diversas noções de
independência espalhadas pelos mais variados campos da Matemática...
Schur Complements and Their Closure
Properties
2005-02-14
Speaker: Ronald Smith
(University of Tennessee at Chattanooga, USA)
Area(s): ...
A importância do Libro de Álgebra (1567) de Pedro Nunes
2005-01-25
Speaker: Henrique Leitão (Centro de História das Ciências da Universidade de Lisboa, Lisboa)
-- ...
Hierarchies of Eigenvalues in Principal Submatrices
and Another Recent Result on Nested Minors
2005-01-18
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg,USA)
Area(s): ...
Colorações de arestas em grafos bipartidos e ortogonalidade de tensores
decomponíveis
2004-12-14
Speaker: Maria Manuel Torres
(Universidade de Lisboa)
Seja $G$ um multigrafo bipartido. Uma partição de inteiros não negativos $\lambda_1,\ldots , \lambda_t)$ diz-se admissível para $G$ se existir uma coloração das arestas de $G$ satisfazendo $|U_i|=\lambda_i,\ i=1, \ldots , t.$
O problema da existência e determinação de um máximo no...
Padrões que comutam: O comutador do padrão completo
2004-11-30
Speaker: Graça Marques
(Universidade do Algarve)
Um padrão $P$ é uma matriz com entradas no conjunto $\{*,0\}$, em que $*$ designa uma entrada não
nula. Uma matriz real $A = (a_{i;j})$ pertence a um padrão $P$ se é do mesmo tipo que $P$ e $a_{i;j} \neq 0$ se e só
se a entrada $(i; j)$ de $P$ é $*$. Dois padrões $n\times n$ $P$ e $Q$...
Caracterização de certas matrizes de banda a partir da caracterização de Fiedler para matrizes tridiagonais
2004-11-16
Speaker: Américo Bento (Universidade de Trás-os-Montes e Alto Douro)
Uma caracterização para matrizes tridiagonais simétricas reais (a
menos de uma semelhança permutacional) devida a Miroslav Fiedler
é:
sendo $A$ uma matriz quadrada real simétrica de ordem $n$, tem-se:
$rank(A+D)\geqslant n-1$, qualquer que seja a matriz diagonal $D$
[condição de...
Representações do grupo quântico associado à parte positiva
de uma álgebra de Lie semisimples
2004-11-09
Speaker: Samuel Lopes
(Universidade do Porto)
Em 1985 Drinfeld e Jimbo introduziram uma família de deformações a um parâmetro q da álgebra universal envolvente associada a uma álgebra de Lie g, complexa e semisimples de dimensão finita. Estas álgebras quânticas Uq(g) têm ligações a áreas diversas da matemática e física teórica, como...
Non-associative algebras as the core of a calculus for nonlinear
nonautonomous ODEs
2004-11-02
Speaker: Eugénio Rocha
(Universidade de Aveiro)
Flows of nonautonomous nonlinear ODEs are difficult to deal in
general, since
a nonautonomous vector field do not commute at different instants of time.
We will show
that vector fields and flows as differential geometry objects can be
regarded
as linear operators in a Fréchét...
Realizações matriciais de pares de quadros de Young e palavras de
Yamanouchi
2004-07-06
Speaker: Ricardo Mamede
(Universidade de Coimbra)
Let $(m_1,...,m_t)$ be a nonnegative integral vector, and
$\sigma\in{\cal S} _t$ such that
$(m_{\sigma(1)},...,m_{\sigma(t)})$ is a partition. A Young
tableau ${\cal T}$ of type $(a^0,(m_1,...,m_t),a^t)$ is a sequence
of partitions $(a^0,a^1,...,a^t)$ where...
Representacões induzidas e imanantes
2004-06-08
Speaker: Carlos Gamas
(Universidade de Coimbra)
Seja $\lambda = (\lambda_{1}, \ldots ,\lambda_{s})$, $\lambda_{1}
= \cdots = \lambda_{s-1} \geq \lambda_{s}$, um caracter
irredut\'{\i}vel de $S_{n}$ correspondente \`{a} parti\c{c}\~{a}o
$(\lambda_{1}, \ldots ,\lambda_{s})$ de $n$. Se $A$ \'{e} uma
matriz herm\'{\i}tica semidefinida...
Anéis graduados em geometria algébrica
2004-03-16
Speaker: Jorge Neves (Universidade de Coimbra)
Tendo como pano de fundo o cálculo elementar do anel associado a
um ponto numa curva elíptica, pretendemos ilustrar o papel dos anéis
graduados no estudo global de variedades algébricas polarizadas.
Area(s): ...
Sums of Matrices
2004-03-09
Speaker: Charles R. Johnson
(College of William and Mary,
Williamsburg,USA)
Area(s): ...
Sobre uma conjectura acerca da inércia de
certas matrizes tridiagonais
2004-03-02
Speaker: Carlos Fonseca (Univ. Coimbra)
Apresentam-se alguns resultados recentes sobre a inércia de certas
matrizes tridiagonais com um determinado padrão antipodal, baseado numa
conjectura de J.H. Drew, C.R. Johnson, D.D. Olesky e P. van den Driessche
(Spectrally arbitrary patterns. LAA, 308(2000), 121-137).
...
A propriedade comutativa dos triângulos de
Littlewood-Richardson
2003-12-16
Speaker: Olga Azenhas
(Univ. de Coimbra)
?? apresentada uma involução no conjunto dos
triângulos
de Littlewood-Richardson.
Esta involução exibe a conhecida simetria
$N_(a,b)^c=N_(b,a)^c$
dos coeficientes de
Littlewood-Richardson. Area(s): ...
Incursões num mundo matemático ao lado do meu
2003-11-25
Speaker: António Guedes de Oliveira
(Universidade do Porto)
Vou descrever alguns problemas matemáticos em que trabalhei
recentemente.
Estão fora do meu âmbito de trabalho habitual, e têm uma boa dose de
ingenuidade.
Parte do trabalho foi feita em colaboração com alunos não-graduados.
Area(s): ...
Alguns
Invariantes de Matrizes com Vários Blocos
Prescritos
2003-11-11
Speaker: Glória Cravo
(Universidade da Madeira)
Come\c{c}amos por descrever os poss\'{i}veis valores pr\'{o}prios de uma
matriz do tipo $pk\times pk$, particionada em $k\times k$ blocos de tamanho $%
p\times p$ quando $2k-3$ blocos est\~{a}o fixos e os restantes variam.
De seguida s\~{a}o descritos os poss\'{i}veis...
Quando é que duas matrizes são semelhantes?
2003-10-14
Speaker: José Carlos Santos
(Universidade do Porto)
Dadas duas matrizes quadradas com a mesma dimensão, como se pode
determinar se são ou não semelhantes Naturalmente, basta determinar as
suas formas canónicas de Jordan e compará-las, mas este método é pouco
prático. Por outro lado, sabe-se que há funções polinomiais, tais como
...
What are the bad 2-letters words?
2003-09-30
Speaker: Charles R. Johnson
(College of William and Mary, Williamsburg,USA)
Area(s): ...
Comparing Schur algebras
2003-07-21
Speaker: Steffen Koenig (University of Leicester)
Area(s): ...
Yangians and W-algebras
2003-07-18
Speaker: Alexander Kleschev (University of Oregon)
Area(s): ...
Applications of clusters to canonical bases
of quantum groups
2003-07-11
Speaker: R. W . Carter (University of Warwick, UK)
An account of work of Marsh and Reinecke.
Area(s): ...
Clusters of finite type
2003-07-10
Speaker: R. W. Carter (University of Warwick, UK)
An exposition of some recent work of Fomin
and Zelevinsky
Area(s): ...
A survey of Green functions
2003-06-20
Speaker: Bhama Srinivasan (University of Illinois,
Chicago, USA)
Area(s): ...
Acção do grupo simétrico num conjunto de
tableaux de Young com realização matricial
prescrita
2003-05-13
Speaker: Ricardo Mamede
Area(s): ...
Desigualdades de entrelaçamento de valores próprios de matrizes
2003-04-02
Speaker: António Leal Duarte
Area(s): ...
Estrutura local dos sistemas holónomos regulares
2003-03-12
Speaker: Pedro C. Silva (Centro de Matemática e Aplicações Fundamentais/Instituto Superior de Agronomia, Lisboa)
Os sistemas holónomos constituem uma classe de sistemas de equações lineares às derivadas parciais sobredeterminados, ou seja, se acrescentarmos uma nova equação não redundante obtemos o sistema trivial (situação análoga às dos sistemas de equações lineares determinados).
Um importante...
Products of Matrices
2003-02-18
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg, USA)
Area(s): ...
On the Numerical Range of some Tridiagonal matrices
2002-12-13
Speaker: Ilya Spitkowsky (Department of Mathematics, College of William and Mary)
Area(s): ...
Anéis de Witt e representações de grupos unitriangulares finitos
2002-12-11
Speaker: Carlos André (Universidade de Lisboa)
No início da década de 60, A. Kirillov desenvolveu o método das órbitas coadjuntas, que permitiu descrever as representações unitárias irredutíveis de qualquer grupo de Lie nilpotente à custa das órbitas sobre o espaço dual da sua álgebra de Lie. No início da década de 70, este método foi...
Monóides solúveis
2002-10-30
Speaker: Manuel Delgado
O núcleo Abeliano KAb(M) de um monóide finito M consiste de elementos de M que de algum modo estão relacionados com
o elemento neutro de qualquer grupo Abeliano finito. Se G for um grupo, KAb(G) é o derivado G' de G. Por analogia com o
caso dos grupos, em que derivados sucessivos podem ser...
Relação entre o grafo de uma matriz e a sua característica de altura
2002-10-23
Speaker: Filipe Alexandre dos Santos
Poder-se-á dizer que tudo começou com Frobenius em 1912, que estabeleceu, ao que se poderia chamar, a primeira relação
entre o grafo duma matriz e a sua raiz de Perron e respectivas multiplicidade algébrica e geométrica. Tal resultado levou a que
muitos matemáticos se debruçassem sobre o...
GPS Differential Positioning using Orthogonal Transformations
2002-06-27
Speaker: Chris Paige (Computer Science, McGill University, Montreal, Canada)
(reporting on joint work with Xiao-Wen Chang)
The Global Positioning System (GPS) is an all weather, worldwide, continuous coverage, satellite based navigation system. GPS satellites transmit signals that allow one to determine, with great accuracy, the location of GPS receivers. In GPS...
Optimizing quadratic forms of adjacency matrices of trees
2002-05-22
Speaker: Wai-Shun Cheung (Centro de Estruturas Lineares e Combinatórias, Universidade de Lisboa, Portugal)
Let G=(V,E) be a tree with n vertices. For n nonnegative numbers
x1= x2 ... = xn= 0,
there exists a mapping \sigma: V -- {x1,...,xn} which maximizes $\sum \sigma(v)\sigma(w)$, where the sum is over all the edges (v,w) of G . A necessary and sufficient condition is determined for...
Contradomínio Numérico e Desigualdades Matriciais em Física
2002-05-15
Speaker: Rute Lemos (Universidade de Aveiro, Portugal)
Area(s): ...
Preservadores lineares do contradomínio determinantal
2002-05-08
Speaker: Graça Soares
Area(s): ...
Acção do grupo simétrico num conjunto tableaux de Young: uma versão matricial
2002-04-24
Speaker: Ricardo Mamede
Area(s): ...
Um minorante para o grau do polinómio mínimo do produto de Kronecker
2002-04-10
Speaker: Cristina Caldeira
Area(s): ...
The Sylvester Equation
2002-04-02
Speaker: Rajendra Bhatia (Indian Statistical Institute, New Delhi, India)
Area(s): ...
Nullities of submatrices of a generalized inverse
2002-03-20
Speaker: R. B. Bapat (Indian Statistical Institute, New Delhi, India)
Area(s): ...
Congruência de matrizes II
2002-02-20
Speaker: Susana Furtado (Faculdade de Economia, Universidade do Porto, Portugal)
Area(s): ...
Congruence of Matrices
2002-02-13
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg, USA)
Area(s): ...
Optimização de funções matriciais
2002-01-16
Speaker: Fátima Leite (Universidade de Coimbra, Portugal)
Area(s): ...
Sistemas de equações diferenciais lineares versus representações lineares de grupos discretos
2001-11-23
Speaker: Orlando Neto (Universidade de Lisboa, Portugal)
O objectivo deste seminário é fazer um survey sobre algumas interacções recentes entre estes dois campos. Serão focados alguns problemas clássicos de Álgebra Linear. Area(s): ...
Invariantes de semelhança de produtos de Jordan: alguns resultados
2001-11-14
Speaker: Enide Martins (Universidade de Aveiro, Portugal)
Area(s): ...
Álgebras de Lie e decomposições de matrizes
2001-10-24
Speaker: Pedro Freitas (Universidade de Lisboa, Portugal)
Veremos como alguns teoremas gerais em álgebras de Lie e espaços simétricos generalizam algumas decomposições bem conhecidas de matrizes. Area(s): ...
O problema do homomorfismo para monóides de traços
2001-10-12
Speaker: Pedro Silva (Universidade do Porto, Portugal)
O problema de determinar se uma função de domínio finito pode ou nâo ser estendida a um homomorfismo entre dois monóides de traços (monóides parcialmente comutativos livres) é indecidível. No entanto, é possivel provar a decidibilidade se o monóide de partida for livre. Como consequência,...
Differentiation of operator functions
2001-06-19
Speaker: Rajendra Bhatia (Indian Statistical Institute, New Delhi, India)
Area(s): ...
Operadores lineares que preservam o contradomínio numérico na álgebra das matrizes triangulares nxn
2001-06-13
Speaker: Maria da Graça Soares (Univ. de Trás-os-Montes e Alto Douro, Portugal)
Area(s): ...
Imanentes
2001-06-06
Speaker: Carlos Gamas
Area(s): ...
Representations of the MONSTER
2001-05-15
Speaker: Roger Carter (Univ. Warwick, UK)
The MONSTER is the largest of the sporadic finite simple groups. In 1979 Conway and Norton published a remarkable conjecture relating representations of the MONSTER to the theory of modular forms. In 1998 Borcherds was awarded a Fields Medal for (among other things) his proof of the...
Polinómios de caminho
2001-03-28
Speaker: Carlos Fonseca
Area(s): ...
Eigenvalues, Graphs and Multiplicities
2001-01-23
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg, USA)
Area(s): ...
Números de Gelfand e de Bernstein da Identidade em R3 para certo tipo de normas
2000-12-13
Speaker: Rosa Amélia Martins (Univ. Aveiro, Portugal)
Usando uma norma p de Hölder no domínio e a norma euclidiana no codomínio prova-se que há igualdade entre os segundos números de Gelfand e de Bernstein para 14. Area(s): ...
Duas questões sobre caracteres de grupos unitriangulares finitos
2000-11-07
Speaker: Carlos André (Universidade de Lisboa, Portugal)
Area(s): ...
Valores próprios multiplos de matrizes cujo grafo é uma árvore
2000-09-27
Speaker: António Leal Duarte
Area(s): ...
Uma generalização do Teorema de Cauchy-Davenport
2000-06-14
Speaker: Hemar Godinho (Universidade de Brasilia, Brasil)
Area(s): ...
Sobre uma involução no conjunto dos tableaux de Littlewood-Richardson
2000-05-17
Speaker: Olga Azenhas
Area(s): ...
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