Seminars
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Historic
On \(C^2\)-actions on complex surfaces
2024-04-24
Speaker: Aram Diaw (CMUP, Univ. Porto)
Given a complex surface \( S \), we are interested in the description of an \( C^2 \)- action on \( S \). It is well-known that this kind of action can be seen as the group of transformations given by the global flows of a pair of commuting complete vector fields. Our goal is to...
Lie groupoids: between equivariant and non-commutative geometry
2024-02-28
Speaker: Bjarne Kosmeijer (Univ. Amsterdam, Netherlands)
Lie groupoids are important objects in the study of symmetries, because they encode a broader notion of symmetries than just actions of Lie groups.
It is important, for instance in the context of index theory, to understand the equivariant geometric aspects of a Lie groupoid.
For Lie...
Reduction by symmetry in Riemannian homogeneous spaces with applications to path-planning
2024-01-30
Speaker: Jacob Goodman (Nebrija Univ., Spain)
In this talk, we derive the necessary conditions for optimality in a second-order variational problem on Riemannian homogeneous spaces by making use of the second fundamental form, reinterpreted as a connection on a horizontal distribution on the underlying Lie group. We assume that the...
Geometric integrators for Riemannian cubic splines
2024-01-30
Speaker: Alexandre Anahory Simões (IE School of Science and Technology, Spain)
Riemannian cubic polynomials are a generalization of splines to Riemannian manifolds with applications in optimal control problems and interpolation problems. Riemannian cubic polynomials are obtained as the curves minimizing a higher-order functional depending on the covariant acceleration...
Structure-preserving integrators in Poisson geometry
2024-01-15
Speaker: Oscar Cosserat (Univ. Gottingen, Germany)
A geometric integrator is a numerical method that preserves the geometric properties of the flow of a differential equation. The rise of geometric integrators stems from the geometrization of mechanics and the development of numerical analysis. I will explain here their relevance within the...
Discrepancy of stratified samples from partitions of the unit cube
2023-11-29
Speaker: Florian Pausinger (Queen's Univ. Belfast, Northern Ireland)
Jittered sampling is a classical way of generating structured random sets in a d-dimensional unit cube. Such sets combine the simplicity of fixed grids with certain probabilistic properties of sets of i.i.d uniformly distributed points and are thus a popular choice in numerical...
On the Dorfman connections of a Courant algebroid
2023-11-29
Speaker: Fani Petalidou (Aristotle Univ. Thessaloniki, Greece)
In this talk, after a short introduction to Courant algebroids and the related algebras defined by them, we will present the notion of Dorfman connection of a Courant algebroid on a vector bundle and some basic results about this. Then, we will present the role of such connections in...
Volume bounds on canonical lift complements of random geodesics
2023-10-18
Speaker: Didac Martinez Granado (Univ. of Luxembourg)
Given a filling closed geodesic on a hyperbolic surface, one can consider its canonical lift in the projective tangent bundle. Drilling this knot, one obtains a hyperbolic 3-manifold. In this talk we are interested in volume bounds for these manifolds in terms of geometric quantities of the...
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...
Towards a general obstruction theory for geometric structures?
2023-05-03
Speaker: Giorgio Trentinaglia (CAMGSD, Univ. Lisboa)
Explicit criteria for the existence of geometric structures on manifolds are known in specific cases and may be understood as special solutions to a certain problem in classical obstruction theory. Adopting Cartan's (and Ehresmann's) views on differential geometry, geometric structures may...
Normal forms in Poisson geometry
2023-03-29
Speaker: Ioan Marcut (Univ. Nijmegen, Netherlands)
This is an introductory talk to Poisson geometry, with a focus on normal forms for Poisson structures. First, we will discuss Weinstein's Splitting theorem and the linearization problem around points, including Conn's theorem. Then I will discuss some of the problems I have worked on:...
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...
Transverse densities and modular classes of Lie groupoids
2023-02-22
Speaker: João Nuno Mestre (CMUC, Univ. Coimbra)
The modular class of a Lie groupoid is a generalization of the modular class of a Lie group, which detects the failure of the Haar measure to be bi-invariant.Certain (good) functors on vector spaces, for example volume elements, and densities, lead to 1-dimensional representations of Lie...
Computing generalized Seifert matrices for closures of colored braids
2023-01-05
Speaker: José Pedro Quintanilha (Univ. Bielefeld, Germany)
Seifert matrices have been a foundational tool in knot theory ever since they were introduced in the 1930's. They are not link invariants - in fact, the definition of a Seifert matrix for a link L depends heavily on the choice of a Seifert surface S for L and of a Z-basis of H_1(S)....
The homology language of a higher-dimensional automaton
2022-11-30
Speaker: Thomas Kahl (CMUM, Univ. Minho)
Higher-dimensional automata, i.e., labeled precubical sets, are a very expressive combinatorial-topological model for concurrent systems. In this seminar, I will talk about the homology language of a higher-dimensional automaton, which is defined as the image of a labeling homomorphism from...
Completeness and linearization
2022-11-16
Speaker: Matias del Hoyo (Univ. Federal Fluminense, Brazil)
Given a surjective submersion, the following are equivalent: (i) it is locally trivial, (ii) it admits a complete connection, (iii) it admits a fibered complete metric. Surjective submersions are examples of Lie groupoids, and conversely, any Lie groupoid can be regarded as a surjective...
Dirac structures and Hamiltonian inverse problem, applications to linear systems and Lotka-Volterra equations
2022-11-09
Speaker: Hassan Alishah (Univ. Minas Gerais, Brazil)
In this talk, I, first, will provide some preliminary definitions and observations on Dirac/big-isotropic structures and Hamiltonian inverse problem. Then I will present an algorithm to solve the Hamiltonian inverse problem for a given system written in the gradient form. Then I will discuss...
Combinatorial properties of link quandles
2022-07-27
Speaker: Manpreet Singh (CAMGSD, IST, Univ. Lisboa)
Classical knot theory is the study of smooth embeddings of circles in the 3-sphere up to the ambient isotopy. One of the fundamental problems in this field is the classification of knots, for which one needs invariants. The fundamental group of a knot complement space is a...
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...
Lie groupoids for PDE analysis
2022-06-29
Speaker: Ivan Beschastnyi (CIDMA, Univ. Aveiro)
Lie groupoids are effective tools for studying singular spaces, which explains their popularity in Poisson geometry, foliation theory and other fields of mathematics. They serve as natural desingularisations and come with an array of useful tools. In recent years, it was understood that...
Geometry of mechanical systems with constraints and impacts
2022-05-04
Speaker:
Anthony Bloch (Univ. of Michigan, USA)
In this talk I will discuss some of the general theory of mechanical (Lagrangian and Hamiltonian) system on manifolds and in particular discuss how the dynamics is affected when there are nonholonomic (nonintegrable) constraints and impacts. I will discuss conservation laws, conservation of...
G-structures on orbifolds
2022-03-04
Speaker: Sebastián Daza (PhD student, CMUC)
Orbifolds allow us to model spaces like manifolds, but with good singularities on them, encoded by finite group actions. If these actions are effective, the frame bundle of an orbifold has a manifold structure. Besides, a linear geometric structure induces a symmetry (group action) on the...
Blow-ups of Lie groupoids and Lie algebroids
2022-03-04
Speaker: Lennart Obster (PhD student, CMUC)
In the presentation, we will go into the (projective) blow-up construction for Lie groupoids and Lie algebroids. In the literature, there are different methods to be found on how to do this, especially for Lie groupoids. The main goal of the talk will be to explain the blow-up construction...
Deformations of symplectic foliations via Dirac geometry and L-infinity algebras
2022-02-16
Speaker: Alfonso Tortorella (CMUP, Univ. Porto)
In this talk, based on joint work with Stephane Geudens and Marco Zambon, we develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result is that each symplectic foliation is attached with a cubic L-infinity...
Non-orientable surfaces in 4-dimensional manifolds and rectangles inscribed in Jordan curves
2022-01-12
Speaker: Peter Feller (ETH, Switzerland)
Toeplitz asked whether every Jordan curve in the Euclidean plane contains 4 points that form the corners of a square? More generally, what about the corners of a rectangle with prescribed aspect ratio? The latter question was recently answered by Greene-Lobb for smooth Jordan curves, but...
Dynamical implications of convexity beyond dynamical convexity
2021-11-17
Speaker: Leonardo Macarini (IST, Portugal)
We will show sharp dynamical implications of convexity on symmetric spheres that do not follow from dynamical convexity. It allows us to furnish new examples of dynamically convex contact forms that are not equivalent to convex ones via contactomorphisms that preserve the symmetry. Moreover,...
Quinn Finite Total Homotopy TQFT as a once-extended TQFT
2021-10-27
Speaker: João Faria Martins (Univ. Leeds, UK)
Quinn Finite Total Homotopy TQFT is a TQFT that works in any dimension and that depends on the choice of a homotopy finite space $B$ (e.g. $B$ can be the classifying space of a finite group or of a finite 2-group). I will report on ongoing joint work with Tim Porter on once-extended versions...
Jones polynomial, Khovanov homology and its geometrization
2021-04-09
Speaker: Marithania Silvero (Univ. Seville, Spain)
Knot Theory studies the classification of knots and links. Jones polynomial, introduced by Vaughan Jones in 1984, was one of the greatest breakthrough in this area, since it was the first polynomial knot invariant allowing to distinguish a knot from its mirror image. At the end of the past...
Peg Problems
2021-03-17
Speaker: Joshua Greene (Boston College, USA)
Toeplitz asked in 1911 whether any Jordan curve in the Euclidean plane contains the vertices of a square. The problem remains open, but it has given rise to many interesting variations and partial results. I will discuss the proof of a related result which is best possible when the curve...
The deformation cohomology of a symplectic groupoid
2021-02-17
Speaker: João Nuno Mestre (CMUC, Univ. Coimbra)
Symplectic groupoids are geometric objects that function as global counterparts to Poisson manifolds, in the same way that Lie groups are global counterparts to Lie algebras.In this talk I will first give an idea of how that analogy works, and I will present the construction of the...
Wallach spaces and Dirac operators
2021-01-20
Speaker: Ana Cristina Ferreira (CMAT, Univ. Minho)
Generalized Wallach spaces are homogeneous spaces of type III, sometimes also called tri-symmetric spaces in the literature. The 'original' Wallach spaces are those of positive sectional curvature and there exist only three of them in dimensions 6, 12 and 24. The three cases are related to...
Link invariants from finite crossed modules and a lifting of the Eisermann invariant
2020-11-16
Speaker: Roger Picken (IST, Univ. Lisbon)
This talk is based on work with João Faria Martins (Univ. Leeds) [1] and several projects with students. I will describe the construction of an invariant of tangles and framed tangles which takes values in an arbitrary crossed module of finite groups. This involves the fundamental...
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...
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...
Quantum matrix algebras: a review
2020-01-06
Speaker: Dmitry Gurevich (Valenciennes Univ., France)
I plan to define certain well-known and new quantum matrix algebras (for instance, Generalized Yangians) and discuss their properties.In particular, I'll consider the problem of defining quantum determinants and other symmetric polynomials in all of them. Also, I'll exhibit some...
The prevalence of persistent tangles
2019-10-23
Speaker: Pedro Lopes (IST, Univ. Lisboa)
This talk addresses persistent tangles. These are tangles whose presence in a knot diagram forces that diagram to be knotted. We provide newmethods for constructing persistent tangles. Our techniques rely mainly on the existence of non-trivial colorings for the tangles in question. Our main...
The homotopy type of shifted cotangent bundles
2019-07-12
Speaker: Ricardo Campos (Univ. Montpellier, France)
Given a vector bundle E over a smooth manifold M, the algebra of functions on its shifted cotangent bundle T*[1]E has a natural structure of a Lie algebra and solutions of the Maurer-Cartan equation correspond to Lie algebroid structures on E. Allowing E to be a dg bundle (bundle of chain...
The geometry of generalized flat ribbons
2019-06-12
Speaker: Matteo Raffaelli (CMUC)
In this talk we will be studying the problem of approximating -- locally along a curve -- a given surface S in three-space by a developable (i.e., flat) one. Naturally, we will consider tangent approximations, where the approximating strip-shaped surface, or ribbon, has the same distribution...
Spin-orbit coupling in the Solar System
2019-04-24
Speaker: Alexandre C. M. Correia (DFUC, Univ. Coimbra)
Recent developments in the study of the Solar System dynamics have shown that it is not such a quiet place. Mutual interactions between all bodies may destabilise the orbits and the spins of all terrestrial planets and satellites. Chaotic motion is everywhere and our present quiet Earth will...
Lagrangian systems with external forces preserving geometric structure
2019-04-24
Speaker: David Martin de Diego (ICMAT, Madrid, Spain)
In this talk we will discuss the geometric description of mechanical systems with external forces. Some of these systems has additional geometric features and we will study if it is possible to preserve some of these properties using geometric integrators like variational integrators...
Geometric constructions: some working hypotheses
2019-04-02
Speaker: Graziani Pierluigi (Univ. of Urbino Carlo Bo, Italy)
Among the many theses regarding the nature of Greek mathematics, the most popular one held by historians and philosophers of ancient mathematics is that Greek mathematics, in particular Euclid's Elements, has a constructive nature. However, it is not always clear what the defenders of this...
Geometry of mechanical control systems with applications
2019-01-23
Speaker: Sandra Isabel Ventura Ricardo (UTAD, Vila Real)
In this talk, a geometric setting for studying mechanical control systems is presented. A special class is distinguished: the class of geodesically accessible mechanical systems, for which the uniqueness of the mechanical structure is guaranteed (up to an extended point transformation)....
On the topological complexity of surfaces
2018-12-05
Speaker: Lucile Vandembroucq (Univ. do Minho)
In this talk, we will consider the concept of topological complexity introduced by M. Farber to give a measure of the motion planning problem and discuss it for surfaces. In particular, we will see that the topological complexity of the Klein bottle and higher genus non-orientable surfaces...
Jacobi multipliers and nonholonomic Lagrangian systems
2018-09-26
Speaker: Patrícia Santos (ISEC, Coimbra)
Jacobi multipliers is a tool in the solution of problems in mechanics that provides Lagrangians descriptions and constants of motion for systems of ODE. In this seminar we establish the relation between Jacobi multipliers and nonholonomic Lagrangian systems where the dynamics is determined...
Infinitesimal automorphisms of VB groupoids and algebroids
2018-06-27
Speaker: Alfonso Tortorella (KU Leuven, Belgium)
VB-groupoids and algebroids are vector bundle objects in the categories of Lie groupoids and Lie algebroids respectively, and they are related via the Lie functor. VB-groupoids and algebroids play a prominent role in Poisson and related geometries. In this talk, based on joint work with...
Minimum energy curves in fluid environments
2018-04-13
Speaker: Luis Machado (ISR/UC and Univ. Trás-os-Montes e Alto Douro)
In path planning problems of autonomous underwater or aerial vehicles is frequently required to find a mission path that minimizes acceleration and drag while a vehicle moves from an initial position to a final target.Drag is a mechanical force that characterizes the resistance that the...
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...
Jacobi structures with a non-exact twist
2017-12-06
Speaker: Cornelia Vizman (West Univ. Timisoara, Romania)
We introduce a concept of twisted Jacobi structure that extends the twisted Jacobi structure of Petalidou and Nunes da Costa, as well as the twisted Poisson structure in wide sense (i.e. with an arbitrary 3-form).We explain the one-to-one correspondence between...
Deformations of coisotropic submanifolds in Jacobi manifolds
2017-10-11
Speaker: Alfonso Tortorella (CMUC, Univ. Coimbra)
Originally introduced by Kirillov and Lichnerowicz, Jacobi manifolds encompass, unifying and generalizing, locally conformal symplectic/Poisson manifolds and (non-necessarily coorientable) contact manifolds. In this talk, in order to investigate the coisotropic deformation problem, we attach...
Variational obstacle avoidance problem on Riemannian manifolds
2017-07-11
Speaker: Margarida Camarinha (CMUC, Universidade de Coimbra)
Motion planning with obstacle avoidance is an important task in the field of robotics. Many methods for autonomous vehicle navigation with obstacle avoidance have been developed in the last few decades. I will talk about a variational obstacle avoidance problem on a Riemannian manifold and...
Nonorientable hypermaps
2017-06-13
Speaker: Daniel Marques Pinto (CMUC, University of Coimbra)
Topologically, a hypermap is a cellular embedding of a connected hypergraph into a closed connected surface. If that underlying surface is orientable, we say that the hypermap is orientable. Otherwise, the hypermap is called nonorientable. We will present some results about nonorientable...
Singularities of non-commutative integrable systems
2017-05-30
Speaker: Rui Loja Fernandes (Univ. of Illinois at Urbana-Champaign, USA)
Integrable systems that appear in "nature" always have singularities and there is a well-known theory of non-degenerate singularities, which are divided into 3 classes: elliptic, focus-focus and hyperbolic classes. However, in the case of non-commutative integrable systems, such a...
Graph complexes and configuration spaces of points
2017-04-19
Speaker: Ricardo Campos (ETH Zürich, Switzerland)
Given a manifold M, one can study the configuration space of n points on the manifold, which is the subspace of M^n in which two points cannot be in the same position. The study of these spaces from a homotopical perspective is of interest in very distinct areas such as algebraic topology or...
An introduction to \(L_\infty\) algebras and \(L_\infty\) algebroids
2017-04-19
Speaker: Raquel Caseiro (CMUC/Univ. Coimbra)
\( L_\infty \) algebras are natural generalizations of Lie algebras from a homotopy theoretical point of view. The original definition dates back to 1992 by J. Stasheff and T. Lada and the idea is to weaken the condition imposing that the Lie bracket satisfies the Jacobi identity. Instead...
The deformation cohomology of a Lie groupoid and applications to rigidity
2017-02-10
Speaker: João Nuno Mestre (CMUC/Univ. Coimbra)
In this talk we discuss deformations of Lie groupoids and introduce the cohomology which controls them. We then study some of its properties, and give a geometric interpretation for it in low degrees. We will also look at relations with other cohomologies: deformation cohomologies for...
A geometric glimpse to certain classes of first order PDE's
2017-01-26
Speaker: Franco Magri (Univ. degli Studi di Milano-Bicocca, Italy)
The purpose of the talk is to illustrate , on a simple example, how ideas from the theory of singularities, from the theory of Riemannian and Frobenius manifolds, and from Hamiltonian mechanics beautifully intertwine in the study of certain classes of first order PDE's of hydrodynamic...
Some tools for the study of Cartan connections on proper Lie groupoids
2016-12-16
Speaker: Giorgio Trentinaglia (IST, Lisboa)
I will describe some results of mine suggesting a clear strategy for the study of the following basic questions - about which little seems to be known - concerning Cartan (i.e. multiplicative) connections on proper Lie groupoids: a) What are the obstructions to the existence of Cartan...
On locally conformal symplectic manifolds of the first kind
2016-12-06
Speaker: Juan Carlos Marrero (Univ. of La Laguna, Tenerife, Spain)
In this talk, I will present some recent results on locally conformal symplectic manifolds of the first kind. In fact, under certain topological restrictions related with the compactness of the canonical foliation, we will discus a structure theorem for these manifolds. In the non compact...
Transverse measures and densities for Lie groupoids
2016-10-26
Speaker: João Nuno Mestre (CMUC, Univ. Coimbra)
We explain how extending Haefliger's approach to transverse measures for foliations to general Lie groupoids allows us to define and study measures and geometric measures (densities) on differentiable stacks. The abstract theory works for any differentiable stack, but it becomes very...
Geometric and numerical methods for optimal control of mechanical systems
2016-06-15
Speaker: Leonardo Colombo (Univ. Michigan, USA)
Under some mild regularity conditions, optimal control problems can be understood as higher-order variational problems. The aim of this talk is to give a general overview on the use of techniques concerning Geometric Mechanics and Geometric Numerical Integration to solve optimal control...
Nijenhuis deformation of Gerstenhaber algebra and Poisson Quasi-Nijenhuis algebroids
2016-04-27
Speaker: Mohammad Jawad Azimi (CMUC/Univ. Coimbra)
The importance of Nijenhuis tensor on the Lie algebra of vector fields on a manifold is not only because of the Newlander-Nirenberg theorem, but also it appears in the study of Hamiltonian systems. The notion is known for some geometric structures such as Poisson manifolds, Courant...
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...
Singular foliations and Lie-infinity algebroids
2016-03-04
Speaker: Camille Laurent-Gengoux (Univ. Lorraine, France)
We will describe a natural L-infinity structure associated to a singular foliation, and explain why they give the geometry of the foliation, like its monodromy. We shall relate this to several classical constructions using Lie groupoids or bisubmersions. Joint work with Sylvain Lavau and...
Toric constructions of monotone Lagrangian submanifolds in CP^2 and CP^1 x CP^1
2016-01-27
Speaker: Agnès Gadbled (Univ. Porto)
In a previous paper, I proved that two very different constructions of monotone Lagrangian tori are Hamiltonian isotopic inside $\mathbb{CP}^2$ by comparing both of them to a third one called modified Chekanov torus. This modified Chekanov torus has an interesting projection under the...
Groupoids, fibrations and rigidity
2015-10-28
Speaker: Matias del Hoyo (IMPA, Brazil)
Fibred categories were introduced in descent theory by A. Grothendieck. In this talk I will discuss fibred Lie groupoids, an incarnation of that formalism in differential geometry, studied by K. Mackenzie, among others. In a joint work with R. Fernandes we construct suitable metrics on...
Heegaard genus and rank of link complements
2015-09-30
Speaker: Darlan Girão (Univ. Federal Ceará, Brazil)
In this talk we will discuss the relationship between the Heegaard genus and rank of 3-dimentional manifolds. Despite some recent advances in this topic, little is known for manifolds arising as link complements in S^3. We will provide a very rich class of link complements for which rank...
Nearly Sasakian manifolds and related structures.
2015-09-08
Speaker: Giulia Dileo (Univ. Bari, Italy)
Nearly Sasakian manifolds are a special class of almost contact metric manifolds, providing a natural odd dimensionalcounterpart of nearly Kähler manifolds.In the present talk I will describe the main properties of nearly Sasakian manifolds, referring also to geometric structures which...
Height functions on symmetric spaces
2015-07-09
Speaker: María José Pereira-Sáez (Univ. Coruña, Spain)
Morse theory gives us useful techniques to analyze the homotopic structure of a smooth manifold studying some smooth functions on this manifold. This allows us to find the cellular structure of a CW-complex and get some information about its cohomology. We will consider here height...
On displaceability of pre-Lagrangians in toric contact manifolds
2015-07-02
Speaker: Milena Pabiniak (IST Lisboa)
In symplectic geometry one can observe a rigidity of intersections: certain (Lagrangian) submanifolds are forced to intersect each other in more points than an argument from algebraic or differential topology would predict. For example, every compact symplectic toric manifold contains a...
Coistropic reduction for Poisson Lie actions
2015-06-18
Speaker: Chiara Esposito (Univ. Wuerzburg, Germany)
In this talk we present a reduction procedure in the setting of a Poisson Lie group (G,\pi_G) acting on a Poisson manifold (M, \pi). In such cases we can introduce the notion of comomentum map and we show that, under certain conditions, it produces a Hamiltonian action on the...
L-infty graded manifolds, Kapranov manifolds and applications
2015-06-05
Speaker: Camille Laurent-Gengoux (Univ. Lorraine, France)
Several linearization problems can be expressed as the linearization of a L-infty algebra for a particular type, that we call Kapranov manifold.A algebroid cohomology class, called the Atiyah class, plays there a crucial role. Joint works with Mathieu Stiénon, Yannick Voglaire and...
The exact discrete Lagrangian function in the Lie groupoid setting
2015-04-08
Speaker: Juan Carlos Marrero (Univ. de La Laguna, Spain)
In this talk, I will present a definition of the exact discrete Lagrangian function associated with a continuous regular Lagrangian function on the Lie algebroid of a Lie groupoid. A result on variational analysis error in this setting will also be presented. In order to define the exact...
Rolling pseudo-Riemannian submanifolds
2015-03-25
Speaker: André Marques (Instituto Politécnico de Viseu)
We present an overview about rolling motions, subject to non-slip and non-twist constraints, of manifolds which are embedded in pseudo-Riemannian manifolds. Within this general framework, we analyze the individual cases of rolling of pseudo-hyperbolic spaces and quadratic Lie groups. We...
Sasakian nilmanifolds
2015-02-19
Speaker: Antonio De Nicola (CMUC, Univ. Coimbra)
Sullivan's theory of models can be used to get topological invariants of manifolds that are stronger than the de Rham cohomology ring.One defines a model for a manifold as a commutative differential graded algebra (CDGA) quasi-isomorphic to the algebra of differential forms. It is known that...
Kaehler-Lie systems and geometric quantum mechanics
2014-12-04
Speaker: Jesús Clemente-Gallardo (Univ. Zaragoza, Spain)
In this seminar we will study an application of the geometric formulation of Quantum Mechanics to study Lie systems on finite-dimensional complex manifolds. We will present the geometric methods developed to study their superposition rules, time independent constants of motion, Lie...
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...
Hypersymplectic and hyperkähler structures with torsion
2014-06-25
Speaker: Paulo Antunes (CMUC)
We define hypersymplectic structures with torsion (HST) on Lie algebroids and establish a 1-1 correspondence between hyperkähler structures with torsion (HKT) and HST structures. We also obtain a contravariant definition of both HKT and HST structures on Lie algebroids. Additionally, we...
The geometry and topology of random simplicial complexes.
2014-04-23
Speaker: Armindo Pereira da Costa (Univ. Warwick, UK)
In this talk we will explore the topological features of random simplicial complexes. We will introduce two models that extend the Erdős–Rényi model for generating random graphs. Unlike in the one-dimensional case (random graphs), we may...
Virial Theorem in Lagrangian formalism
2014-03-19
Speaker: Patrícia Santos (CMUC/ISEC)
In this talk the geometric approach to the virial theorem in Lagrangian formalism is presented in quasi-velocities, and a generalization of the virial theorem on Lie algebroids is given. The virial theorem was introduced by Clausius in statistical mechanics in 1870 and since then it became...
On the Gromov width of polygon spaces
2014-02-05
Speaker: Alessia Mandini (Univ. of Pavia, Italy)
After Gromov' foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold (M,\omega) is a symplectic invariant that measures, roughly speaking, the size of the biggest ball we can symplectically embed in...
On the contributions of lattice theory to the study of persistent homology.
2013-11-06
Speaker: João Pita Costa (Josef Stefan Institute, Liubliana, Slovenia)
In the past 20 years Topological Data Analysis has been a vibrant area of research a lot due to the developments in applied and computational algebraic topology. Essentially it applies the qualitative methods of topology to problems of machine learning, data mining or computer vision. Under...
Geometric Quantum Mechanics and applications
2013-11-06
Speaker: Jesús Clemente-Gallardo (Univ. Zaragoza, Spain)
We can notice that the approaches to Classical and Quantum Mechanics are quite different in many aspects, the most striking one being the linear structure which is present in the Hilbert space H and which is considered usually as one of the most relevant aspects of the formalism. There are...
Einstein manifolds with skew torsion
2013-10-16
Speaker: Ana Cristina Ferreira (Univ. Minho)
In this talk, we will present a systematic investigation of manifolds that are Einstein for a connection ∇ with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any Einstein manifold with skew torsion has...
A structure theorem for co-Kähler manifolds
2013-09-13
Speaker: Giovanni Bazzoni (Universität Hamburg, Germany)
Co-symplectic and co-Kähler structures are the odd-dimensional analogue of symplectic and Kähler structures. In this talk we shall review the basic concepts of both geometries, which are a special case of almost contact metric structures. We will prove a structure theorem for...
Stability of hyperfinite knots
2013-07-02
Speaker: Pedro Lopes (IST, Lisboa)
A hyperfinite knot is an attempt to make sense of limits of sequences of knots with increasing crossing number.Given a knot invariant taking values on a complete metric space, we define the following quotient space of equivalence classes of knots: two knots are related if, by definition,...
Modular classes and Dirac structures
2013-04-24
Speaker: Raquel Caseiro (CMUC/Univ. Coimbra)
We begin by reviewing some properties concerning modular classes in Poisson and Lie algebroid theory. By generalizing modular classes to Dirac structures, we have a general framework to understand these structures and the reduction example of a Poisson manifold become more clear....
Hom-Lie algebroids
2013-02-20
Speaker: Joana Teles (CMUC/Univ. Coimbra)
We review some definitions and constructions of hom-Lie algebras, hom-associative algebras and hom-Poisson algebras. We define hom-Lie algebroids, a definition that may seem cumbersome at first, but which is justified, first, by a one-to-one corespondence with hom-Gerstenhaber algebras, a...
Instantons on the manifolds of Bryant and Salamon
2012-12-05
Speaker: Andrew Clarke (IME/USP, Brazil)
The first examples of complete manifolds of holonomy G2 were constructed by Bryant and Salamon in the 1980's. More recently, gauge theory on manifolds on reduced holonomy has be introduced and greatly developed. I will explain this theory in the case of G2 holonomy and explain a new...
KAM and presymplectic dynamics
2012-12-05
Speaker: Hassan Alishah (IST, Lisboa)
Classical Kolmogrov-Arnold-Moser theory studies stability problem for invariant tori for nearly integrable dynamical systems. This theory has been developed beyond nearly integrable systems. I will explain basic concepts and results of the classical KAM theorem. Then I will state a KAM...
Vector bundles over Lie groupoids and Lie algebroids
2012-11-21
Speaker: Matias del Hoyo (IST, Lisboa)
In a real vector space addition is settled by scalar multiplication. This makes possible to describe smooth vector bundles as manifolds endowed with a nice action of the multiplicative monoid of the real numbers. In this talk I will deal with vector bundles over Lie groupoids and algebroids....
Primitive Groups are rare (but useful)
2012-10-17
Speaker: Daniel Pinto (CMUC, Univ. Coimbra)
A hypermap is, in its topological form, a cellular embedding of a connected hypergraph. Hypermaps can be modified by some operations, like duality (the operation that interchanges hypervertices and hyperfaces on oriented hypermaps). The notion of duality index was created to measure how far...
Higher analogues of symplectic fibrations
2012-09-19
Speaker: Olivier Brahic (IMPA, Rio de Janeiro, Brazil)
Given a differential form defined on the total space of a fibration, we interpret geometrically the equations for it to be closed. We obtain this an elementary model for higher TFTs, that can be interpreted as parallel transport along surfaces, volumes... Starting from hamiltonian...
The kinematic reduction and Hamilton-Jacobi equation on skew symmetric algebroids
2012-06-12
Speaker: María Barbero Liñán (Univ. Carlos III, Madrid, Spain)
Hamilton-Jacobi theory has strong similarities with kinematic reduction by means of decoupling vector fields of nonholonomic mechanical control systems. We describe that interconnection on a geometric structure called skew-symmetric algebroid, which generalizes the notion...
Hypersymplectic structures on Courant algebroids
2012-06-12
Speaker:
Paulo Antunes (CMUC/Univ. Coimbra)
In this talk, we define hypersymplectic structures on Courant algebroids and show that we recover, as particular cases, all the classical results and examples of hypersymplectic structures on Lie algebroids. As on Lie algebroids, we prove a 1-1 correspondence theorem between hypersymplectic...
Quadratic symplectic Lie superalgebras and Lie bi-superalgebras
2012-05-15
Speaker: Elisabete Barreiro (CMUC/Univ. Coimbra)
Lie bi-superalgebras arise in the theory of quantum mechanical integrable models and are related to the graded classical Yang-Baxter equation. By a triangular Lie bi-superalgebra we mean a Lie bi-superalgebra which co-multiplication comes from an even skew-symmetric solution of the classical...
Integral affine geometry of non-commutatively integrable Hamiltonian systems
2012-05-15
Speaker: Daniele Sepe (IST, Lisboa)
In mechanics there are many Hamiltonian systems which admit more integrals of motion (with suitable properties) than degrees of freedom (e.g. the Euler top). These systems are known as superintegrable or non-commutatively integrable and have been studied extensively since the pioneering...
Pairs of compatible tensors on Courant algebroids and hierarchies
2012-04-17
Speaker: Joana Nunes da Costa (CMUC/Univ. Coimbra)
We show that a Poisson-Nijenhuis structure can be defined on a Courant algebroid as a pair of compatible tensors satisfying several constraints. Other pairs of compatible tensors such as deforming-Nijenhuis and Nijenhuis pairs can also be considered. We construct natural hierarchies of such...
Deformations of Lie groupoids
2012-04-17
Speaker: João Nuno Mestre (Utrecht University)
Deformations of Lie groupoids can be studied by means of the intrinsiccohomology that controls them. This approach is related both to thestudy of deformations of Lie group actions by Palais, and to thelinearization theorem for proper Lie groupoids. We obtain a vanishingresult for the...
On Leibniz algebras and Loday algebroids
2012-03-20
Speaker: Yvette Kosmann-Schwarzbach (École Polytechnique, France)
We shall briefly review Leibniz algebras and their cohomology. We shall then define Loday algebroids, give examples and outline their supergeometric interpretation, following the 2011 preprint by Grabowski, Khudaverdian and Poncin....
Hyperpolygons and moduli spaces of parabolic Higgs bundles
2012-03-20
Speaker: Alessia Mandini (IST, Lisboa)
In this talk I will describe the geometry of the moduli space of polygons and of its hyperkaehler analogue, the so called hyperpolygon space. In particular I will discuss how these spaces are isomorphic to certain moduli spaces of stable, rank-2, parabolic and parabolic Higgs (respectively)...
Tunnel number degeneration under the connected sum of prime knots
2012-02-15
Speaker: João Nogueira (CMUC/Univ. Coimbra)
In this talk, a study on 2-string free tangle decompositions of knots with tunnel number two will be presented. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't...
Geometry and Topology of 3-cosymplectic manifolds
2012-02-15
Speaker: Antonio de Nicola (CMUC)
In this talk, we deal with 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kähler structures, just as cosymplectic manifolds are the closest odd-dimensional analogue of Kähler structures. After a brief introduction to the geometric properties of...
Veering triangulations admit strict angle structures
2011-07-26
Speaker: Henry Segerman (University of Melbourne, Australia)
Agol recently introduced the concept of a veering taut triangulation of a 3-manifold, which is a taut ideal triangulation with some extra combinatorial structure. Hodgson, Rubinstein, Tillmann and I show that each veering triangulation admits a strict angle structure, which is a necessary...
The Calabi-Yau equation for Lagrangian fibrations
2010-12-15
Speaker: Luigi Vezzoni (Università di Torino, Italy)
The Calabi-Yau equation on Almost-Kaehler manifolds is an elliptic equation arising from a natural generalization of the Calabi conjecture to the non-complex context. This equation was introduced by Donaldson who proved that its solutions are unique and Tosatti, Weinkove and Yau proved that...
Sub-semi-Riemannian geometry on Heisenberg-type groups
2010-11-24
Speaker:
Anna Korolko (University of Bergen, Norway)
Sub-semi-Riemannian geometry is a new subject generalizing sub-Riemannian and semi-Riemannian geometries. I will introduce basic notions and facts from the theory of sub-semi-Riemannian geometry, show examples of sub-semi-Riemannian manifolds, namely, some Heisenberg-type...
Legendre foliations on contact manifolds and related topics
2010-09-29
Speaker:
Beniamino Cappelletti Montano (research visitor at CMUC)
In this talk some recent results on the theory of Legendre foliations on contact Riemannian manifolds will be reviewed. In particular, we will discuss about Legendre foliations on Sasakian manifolds, bi-Legendrian structures and contact metric (\kappa,\mu)-spaces. Such results will be...
Graduações das álgebras de Lie simples
2010-09-16
Speaker: Alberto Elduque (Departamento de Matemáticas, Universidade de Saragoça, Espanha)
As graduações para as álgebras de Lie clássicas foram descritas recentemente incluindo o caso modular. Neste conferência apresentam-se as técnicas utilizadas e comentam-se os últimos trabalhos sobre as álgebras de Lie excepcionais. ...
Twisted contact groupoids and integration of twisted Jacobi structures
2010-09-15
Speaker: Fani Petalidou (Aristotle University of Thessaloniki, Grécia)
TBA...
Jacobi structures in supergeometric formalism
2010-07-08
Speaker: Paulo Antunes (FCTUC/CMUC)
In this talk, we state and prove most known results (established by Iglesias-Marrero and Grabowski-Marmo) about Jacobi algebroids and bialgebroids using the supergeometric formalism, more precisely, the so-called "big bracket", a formalism where brackets and anchors are encoded by...
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...
Compact generation for Lie groupoids
2010-06-17
Speaker: Nicolas Raimbaud (Université de Nantes)
In the 80's, André Haefliger introduced the problem of compact realization for foliations -- which is still open, and gave a sufficient condition for realization, the compact generation of the holonomy pseudogroup. We introduce a Morita-invariant notion of compact generation for...
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...
Frobenius manifolds and dispersionless integrable hierarchies
2010-03-09
Speaker: Guido Carlet (CMUC)
We review the construction of the principal hierarchy associated to a Frobenius manifold....
Duality Groups
2010-02-23
Speaker: Daniel Pinto (CMUC/Mat.FCTUC)
TBA...
Compatibilities and Lie algebroid structures. Examples in hyperkähler structures
2010-02-04
Speaker: Paulo Antunes (Dep. Mat. FCTUC/CMUC)
--...
Lie algebroids and related structures in supergeometric terms
2010-02-02
Speaker:
Paulo Antunes (Dep. Mat. FCTUC/CMUC)
--...
Action-angle variables : the Poisson case, around a singular leaf
2010-01-08
Speaker: Camille Laurent-Gengoux (CMUC)
TBA...
Around the Toda lattice
2009-12-02
Speaker: Khaoula ben Abdeljelil (Univ. de Poitiers, France)
We will show the Liouville integrability of differential equations that naturally appear on simple complex Lie algebras. ...
The Extended Toda hierarchy and Frobenius manifolds
2009-11-20
Speaker: Guido Carlet (CMUC)
We will review the definition of Frobenius manifolds and give some hints of their connection with the theory of bi-Hamiltonian integrable equations, focusing on the example of the Extended Toda hierarchy and the quantum cohomology of the Riemann sphere....
Reduction of Poisson-Nijenhuis Lie algebroids
2009-11-13
Speaker: Antonio De Nicola (CMUC)
...
Inner-derivations irreducible LY-algebras
2009-10-16
Speaker: Pilar Benito (Universidade de Logronho, Espanha)
Lie-Yamaguti (LY-algebras) are binary-ternary algebras intimaly related to reductive homogeneous spaces. The LY-algebras which are inner-derivation-irreducible can be described through generalized Tits construction and non-associative systems such as Lie and Jordan algebras, Lie and...
Inner-derivation triple systems and Lie (super)algebras
2009-10-14
Speaker: Pilar Benito (Universidade de Logronho, Espanha)
In 1985 J.R. Faulkner determine which 3-linear identities are satisfied by a large class of derivation-irreducible triple systems. The founded identities and related triples are in the heart of several well-known constructions of simple Lie algebras and superalgebras from Freudenthal to our...
Deformations of integrable spin systems by twist trasformations of quantum groups
2009-05-27
Speaker: Petr P. Kulish (GFM, Universidade de Lisboa, and St. Petersburg Department of Steklov Mathematical Institute)
--...
Lie algebras' relatives: Filippov algebras and Filippov superalgebras
2009-05-22
Speaker: Patrícia Damas Beites (Universidade da Beira Interior)
The notion of n-Lie superalgebra was introduced in 1996, by Daletskii and Kushnirevich, as a natural generalization of the n-Lie algebra concept due to Filippov (1985). Because of the actual tendency of Filippov's scientific followers, we will use the terms Filippov superalgebra and Filippov...
Cyclic branched coverings as invariants for knots
2009-05-20
Speaker: Luisa Paoluzzi (Université de Provence, France)
For each knot in the 3-sphere it is possible to construct an infinite family of topological invariants, the cyclic branched covers of the knot. After describing how these invariants are constructed, I will try to give an overview of the problem of determining how strong these invariants are....
Symplectic groupoids : a way to get rid of singularities
2009-04-22
Speaker: Camille Laurent-Gengoux (Université de Poitiers, France)
...
Lie algebroid Extensions
2009-03-30
Speaker: Olivier Brahic (CAMGSD, IST)
Lie algebroids provide a rather flexible theory. They are relevant for describing many geometric structures such as Poisson, symplectic, or contact manifolds. I will expose the notion of extension for Lie algebroids, and explain how they naturally get involved when studying fibrations with...
New simple modular Lie superalgebras
2009-03-27
Speaker: Alberto Elduque (Universidade de Saragoça, Espanha)
Quite recently the finite dimensional simple modular Lie superalgebras with a Cartan matrix have been classified by Bouarroudj, Grozman and Leites. Most of the new objects that arise in this classification, that is, which are not modular counterparts of the superalgebras in Kac's...
A decomposition theorem for 3-quasi-Sasakian manifolds
2009-03-23
Speaker: Antonio De Nicola (Departamento de Matemática Fundamental, Universidad de La Laguna, Islas Canarias)
...
Poisson reduction via graded geometry
2009-02-27
Speaker: Marco Zambon (CMUP)
A Poisson manifold is a space endowed with a suitable bivector field. Poisson manifolds can be equivalently encoded in terms of so-called graded manifolds. We will use this approach, which conceptually turns out to be very simple and systematic, to obtain new Poisson manifolds out of given...
Constructions on hypermaps
2009-01-21
Speaker: Daniel Pinto (CMUC)
Area(s): ...
Lie algebroids and hamiltonians in supermanifolds
2008-12-16
Speaker: Paulo Antunes (Dep. Matemática, Coimbra)
In this talk, we will first recall the definition and some basic properties of Lie
algebroids. Then we will see that a Lie algebroid corresponds to a function on a
(symplectic) supermanifold and we will use this supergeometric approach to study some
geometry on Lie algebroids.
...
On Poisson quasi-Nijenhuis Lie Algebroids
2008-12-02
Speaker: Antonio De Nicola (CMUC)
After a quick review of the notion of Lie algebroid, the presentation
will focus on a definition of Poisson quasi-Nijenhuis Lie algebroids as
a natural generalization of Poisson quasi-Nijenhuis manifolds.
It will be shown that any such Lie algebroid has an associated...
Singular foliations: Longitudinal pseudodifferential calculus and index theory
2008-11-18
Speaker: Iakovos Androulidakis (CMUP)
A. Connes showed that the space of leaves of a regular foliation can be replaced by the
$C^*$-algebra of its associated holonomy groupoid. However, for a singular foliation the
holonomy groupoid is quite an ill-behaved object. Recently we constructed the
$C^*$-algebra of \textit{any}...
On the geometric (pre)quantization of twisted Poisson manifolds
2008-01-10
Speaker: Fani Petalidou (University of Cyprus)
We study the geometric quantization process for twisted Poisson manifolds. First, we introduce the notion of Lichnerowicz-twisted
Poisson cohomology for twisted Poisson manifolds and we use it in order to characterize their prequantization bundles and to establish their prequantization...
Odd-quadratic Lie superalgebras
2007-12-05
Speaker: Elisabete Barreiro (Dep. de Matemática, FCTUC)
In this talk we will give in detail an inductive description of odd-quadratic Lie superalgebras
such that the even part is a reductive Lie algebra. We will present the construction of odd double extension of
an odd-quadratic Lie superalgebras by the one-dimensional Lie algebra
and ...
The geometry of the diffeomorphisms group on the torus and the Euler flow
2007-10-26
Speaker: Ana Bela Cruzeiro (IST Lisboa)
In the spirit of Arnold's approach to hydrodynamics we study the
geometry of the diffeomorphisms group (in this case of the torus). We
prove that for the 2-dimensional case the Ricci curvature is positive.
Nevertheless probabilistic arguments show that the Euler flow is non...
The Geometry of 3-quasi-Sasakian manifolds
2007-10-19
Speaker: Antonio De Nicola (CMUC)
In the talk I will present the main results of our systematic study of
3-quasi-Sasakian manifolds, conducted in collaboration with B. Cappelletti
Montano and G. Dileo. In particular we prove that the three
Reeb vector fields generate an involutive distribution determining a
canonical...
Applications of quaternionic analysis to Yang-Mills gauge theories
2007-04-11
Speaker: Rolf Krausshar Soeren
(Universidade de Gent, Bélgica)
Area(s): ...
Singularities of holomorphic flows
2007-02-27
Speaker: Helena Reis (CMUP/Faculdade de Economia, Univ. Porto)
Semi-complete vector fields are essentially the local version of complete ones, where blow-up on finite time cannot occur. They represent the vector fields admitting a maximal solution and, consequently, a "flow". The germs of singular foliations associated to these vector fields in...
Acções Parciais de Grupos e Temas Relacionados
2007-02-23
Speaker: Miguel Ferrero (Univ. Federal do Rio Grande do Sul, Brazil)
Vamos definir acções parciais de grupos em conjuntos e a correspondente acção envolvente parcial. Toda a acção parcial em conjuntos possui uma envolvente. Daremos uma ideia da prova desse facto. Também observaremos que acções parciais de grupos estão em correspondência biunivoca com acções...
Construction of symplectic quadratic Lie algebras from Poisson algebras
2007-02-13
Speaker: Said Benayadi (Dep Mat, U Metz, França)
By using the Koecher-Kantor-Tits construction and the notion of double extension of
quadratic Lie algebras, we give a construction of symplectic quadratic Lie algebras
g(A) from an arbitrary Poisson algebra A. In particular, if the dimension of A is
finite, then the dimension...
Poisson structures of quotient varieties and deformations
2006-09-06
Speaker: Jacques Alev (Université de Reims, France)
Area(s): ...
Representações e grupo dos automorfismos de deformações de álgebras de Lie nilpotentes
2006-04-26
Speaker: Samuel Lopes (Fac. Ciências, U. Porto)
As álgebras quânticas (como sejam as quantizações de álgebras envolventes de álgebras de Lie, os grupos quânticos algébricos, as álgebras de Weyl generalizadas e os espaços quânticos afim e simplético) têm cativado o interesse de matemáticos e físicos nos últimos 20 anos. O seu estudo tem-se...
Explicit formulas for the Cauchy and Green kernel functions on some conformally flat manifolds and applications to fluid dynamics
2005-12-07
Speaker: Rolf Soeren KRAUSSHAR
(Departamento de Análise Matemática - Universidade de Gent - Bélgica)
Area(s): ...
Representação de Grupos de Lie em algebróides de Lie e Redução de algebróides de Lie com simetria
2005-11-17
Speaker: Patrícia Santos
(Departamento Física e Matemática - Instituto Superior de Engenharia de Coimbra)
Area(s): ...
On the asymptotic growth of entire solutions to Dirac type equations
2005-10-11
Speaker: Rolf Soren Krausshar
(Departamento de Análise Matemática - Universidade de Gent - Bélgica)
Area(s): ...
Uma teoria de formas automorfas na análise de
Clifford e as suas aplicações a espaços de Hilbert e a problemas
de fronteira
2005-06-29
Speaker: Rolf Soeren KRAUSSHAR
(Departamento de Análise Matemática - Universidade de Gent- Bélgica)
Area(s): ...
Coberturas regulares de um enlace numa
variedade tridimensional
2005-05-04
Speaker: António Salgueiro
(Departamento de Matemática da Universidade de Coimbra, CMUC)
Area(s): ...
Sabinin Algebras: The Basis of a Nonassociative Lie Theory
2005-04-22
Speaker: José Perez Isquierdo
(Universidade de Logronho, Espanha)
Area(s): ...
Courant algebroids and quasi-Poisson linear structures
2005-03-23
Speaker: Fani Petalidou (University of Peloponnese,
Grécia)
Area(s): ...
Structures de Dirac et réduction de variétés de Jacobi
2004-04-22
Speaker: Fani Petalidou (Universidade do Peloponeso, Grécia)
Area(s): ...
Algebróides de Lie e Geometria de Poisson
2004-01-23
Speaker: Paulo Antunes (Departamento de Matemática, Universidade de Coimbra)
Abordaremos a estreita relação entre as noções de algebróide de Lie e algumas das suas generalizações e a geometria das variedades de Poisson.
Area(s): ...
Aplicações harmónicas entre poliedros Riemannianos
2003-05-21
Speaker: Maria Elisabete Félix Barreiro
Area(s): ...
q-deformed Toda lattice and the moqular double of the quantum U_q sl(2) algebra
2003-05-03
Speaker: Michael Semenov-Tian-Shansky (Universidade de Bourgonha, França)
Area(s): ...
Star products on some Classical Double Poisson-Lie groups
2003-05-03
Speaker: Carlos Moreno (Universidade de Madrid, Espanha)
Area(s): ...
Dirac structures: from vector spaces to Lie bialgebroids
2003-04-02
Speaker: Jesus Clemente Gallardo
Dirac structures were introduced by Courant and Weinstein (and in a different framework by Dorfman) in the late eighties, as a generalization of Poisson structures. The simplest examples are defined
on vector spaces, but it is in the framework of Lie algebroids where they are producing the...
Algebróides de Lie e estruturas de Jacobi
2003-02-26
Speaker: Joana Nunes da Costa
Area(s): ...
Álgebras de Cayley e álgebras de Clifford, como álgebras de grupo deformadas
2003-02-05
Speaker: Helena Albuquerque
Nesta palestra estudamos as álgebras deformadas de grupo, como quasiálgebras de divisão associativas. Apresentamos alguns exemplos significativos, estudamos alguns teoremas de classificação e descrevemos as representações para esta classe de álgebras Area(s): ...
Linearização das Estruturas de Poisson
2003-01-22
Speaker: Philippe Monnier (IST, Lisbon)
Area(s): ...
Aplicações dos Algebróides de Lie em Teorias Gauge
2002-12-05
Speaker: Jaime Camaraco, Universidade de Saragoça, Espanha
Area(s): ...
El quadrado mágico de Freudenthal -Tits
2002-07-18
Speaker: Alberto Elduque, Departamento de Álgebra da Universidade de Saragoça, Espanha
Una nueva construccion del Quadrado Mágico de Freudenthal -Tits, que incluye las 5 álgebras de Lie excepcionales, será presentada. Esta construccion utiliza las álgebras de composicion simétricas, que permiten fórmulas muy sencillas para el fenómeno de la trialdad. Area(s): ...
Les Poissons et leurs déformations
2002-01-29
Speaker: Pol Vanhaecke, Poitiers University, France
Area(s): ...
Complex oscillations of Bursting type modeling Physiology and Biology phenomenon
2001-11-21
Speaker: Jean-Pierre Françoise, Paris VI University, France
Area(s): ...
Quadratiques superalgÚbres et reciproques des théorÚmes de Koszul
2001-10-30
Speaker: Said Benaydi, Metz University, France
Area(s): ...
ops(1/2) Gaudin models
2000-10-11
Speaker: Nenad Manojlovic, Universidade do Algarve, Portugal
Area(s): ...
Relativistic epicycles
2000-09-25
Speaker: Richard Kerner, University Pierre et Marie Curie, Paris, France
Area(s): ...
Algumas propriedades do Bar-radical de álgebras Báricas
2000-07-06
Speaker: Henrique Guzzo, University of S. Paulo, Brazil
Area(s): ...
Algebraic geometric aspects of integrable systems
2000-05-26
Speaker: Pol Vanhaecke, University of Poitiers, France
Area(s): ...
Composicion de formas quadráticas
2000-04-28
Speaker: Alberto Elduque, University of Saragoça, Spain
Area(s): ...
Triallity and symmetric composition
1999-06-30
Speaker: Alberto Elduque, University of Saragoça, Spain
Area(s): ...
On the centre of the enveloping algebra of a classical lie superalgebra
1999-06-23
Speaker: Ian Musson, University of Wisconsin, Milwaukee, USA
Area(s): ...
The A-D-E problem, Poisson manifolds and singularities
1999-05-12
Speaker: Pantelis Damianou, University of Cyprus
Area(s): ...
Poisson reduction via graded geometry
Speaker: Marco Zambon (CMUP)
A Poisson manifold is a space endowed with a suitable bivector field.
Poisson manifolds can be equivalently encoded in terms of so-called
graded manifolds. We will use this approach, which conceptually turns
out to be very simple and systematic, to obtain new Poisson manifolds
out of...
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