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Lattice decomposition of modules and decomposition of categories
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 special...
Riemann-Hilbert problems in the theory of orthogonal polynomials
Speaker: Amílcar Branquinho (CMUC, Univ. Coimbra)
In this talk we survey different aspects of the theory of orthogonal polynomials.Due to the ubiquity nature of orthogonal polynomials in modern science, their study has been performed from very many different points of view. Indeed, they can be considered from a purely algebraic point of view, from...
On the existence of solutions for inextensible string equations
Speaker: Ayk Telciyan (UC|UP PhD programme student)
In this talk, we analyze existence of solutions for inextensible string equations. In particular, we have results in two directions.On one hand, we find explicit traveling wave solutions for a system of hyperbolic conservation laws resulting from inextensible string equations via suitable change of...
Representations of fundamental groups of surfaces
Speaker: Peter Gothen (CMUP, Univ Porto)
We consider representations of the fundamental group of a closed surface in the group SL(2,R). To each such representation one can associate an integer invariant called the Toledo invariant. A theorem of J. Milnor says that the absolute value of the Toledo invariant is less than or equal to g-1,...
Campanato spaces and applications in partial differential equations
Speaker: David Jesus (UC|UP PhD Programme student)
In this talk I will discuss a generalization of Campanato's characterization of Holder continuity, and use these results to study the regularity of solutions to the non-homogeneous p-Laplace equation....
Boolean representable simplicial complexes
Speaker: Maria Inês Couto (UC|UP PhD Programme student)
In this seminar we will discuss some properties of a particular class of simplicial complexes from a purely combinatorial perspective. The elements of this class, including all the matroids, admit a representation by a matrix with entries in the boolean semiring, so they are said boolean...
Decidability of first-order theories
Speaker: Cristina Sernadas (CMAFcIO, Univ. Lisboa)
Some results and reduction techniques for proving decidability of mathematical theories and completeness of logics are presented. The crucial role of the theory of real closed ordered fields is explained. Selected illustrations from Euclidean Geometry to Quantum Logic are discussed....
Speaker: Adérito Araújo (CMUC, Univ, Coimbra)
Kippenhahn's Theorem
Speaker: Stephan Weis (CMUC)
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 algebraic...
Speaker: Ivan Yudin (CMUC, Univ. Coimbra)
On the topological complexity of surfaces
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 is...
Truncated boolean representable simplicial complexes
Speaker: Pedro V. Silva (CMUP, Univ. Porto)
These structures constitute the largest known class of simplicial complexes admitting a geometric/topological theory. We will present the main features of this class and some recent results (joint work with Stuart Margolis (Bar-Ilan) and John Rhodes (Berkeley))....
Information lost when resampling
Speaker: Tilo Wiklund (Univ. of Uppsala, Sweden)
Various procedures in statistics rely on taking decisions based on data that has been resampled (usually with replacement). Examples include bootstrap-based confidence bounds and error estimates or "bagged" estimators. Since resampling is an additional source of randomness such resampled...
Variational theory and spectral geometry of quantum graphs
Speaker: James Kennedy (Univ. Lisboa)
The past decade has seen a pronounced growth of interest in differential operators defined on metric graphs, commonly known as quantum graphs. They offer the technical simplicity of one-dimensional objects, while often displaying complex behaviour akin to higher-dimensional ones, and are thus...
Geometry of mechanical control systems with applications
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). Non-linear...
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