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Tag Archives: Seminari Informal de Matemàtiques de Barcelona


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SIMBa: Regular subdivisions and triangulations

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Dimecres 24 d’abril se celebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant: Eva Philippe.
Universitat / Institut de recerca: Sorbonne Université i Universitat de Barcelona.

Data: Dimecres, 24 d’abril de 2024.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: UB (FMI aula IA) and Zoom.
Idioma: Anglès.

Títol: Regular subdivisions and triangulations.

Resum: Subdivisions and triangulations of point configurations in $\mathbb{R}^d$ are a central topic of polyhedral combinatorics and among them regular subdivisions form a particular family which enjoys special geometric properties.
A subdivision is regular if it can be obtained by taking the lower faces of a lifting of its vertices in one dimension higher. This lifting process was central to improve the best known lower bound on the number of combinatorial types of polytopes (joint work with Arnau Padrol and Francisco Santos). Moreover, it happens that among the set of all subdivisions of a fixed point configuration, the regular ones have a particular topological structure. Indeed, they are in correspondence with the faces of a polytope called the secondary polytope.


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SIMBa: Pesin’s theory in a transcendental setting

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Dimecres 3 d’abril se celebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant:   Anna Jové.
Universitat / Institut de recerca: Universitat de Barcelona (UB).

Data: Dimecres, 3 d’abril de 2024.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: FMI (UB): TBA i Zoom.
Idioma: Anglès.

Títol: Pesin’s theory in a transcendental setting.

Resum: Roughly speaking, Pesin’s theory for $\mathbb{R}^n$ diffeomorphisms states that the asymptotical contraction or expansion around almost-every orbit is controlled by the Lyapunov exponents (as long as none of them is zero). For rational maps, this translates into well-defined generic inverse branches around almost-everywhere in the Julia set (Przytycki). In this talk, I will explain the previous statements, and I will discuss its possible generalizations to transcendental maps (Fagella-J.).


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SIMBa: Geometría y topología de espacios de Teichmüller

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Dimecres 20 de març se celebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant:   Alejandro García Sánchez.
Universitat / Institut de recerca: Universitat Autònoma de Barcelona (UAB).

Data: Dimecres, 20 de març de 2024.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: CRM (UAB): aula petita i Zoom
Idioma: Castellà.

Títol: Geometría y topología de espacios de Teichmüller.

Resum: Se construyen los espacios de Teichmüller en el contexto del problema de clasificación de superficies de Riemann cerradas. En primer lugar, analizaremos el primer caso no trivial (género 1), que nos permitirá dotar al espacio de móduli de una rica estructura geométrica vía un espacio que llamaremos de Teichmüller. A partir de ahí, el objetivo es mostrar la generalización para género superior de estos dos espacios y hacer énfasis en la “naturalidad” de estas construcciones, si bien se
evita por completo el tratamiento del tema desde teoría de categorías.


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SIMBa: Splitting of separatrices in generalized standard maps

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Dimecres 6 de març se celebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant:  Dídac Gil Rams.
Universitat / Institut de recerca: Centre de Recerca Matemàtica (CRM).

Data: Dimecres, 6 de març de 2024.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: UPC (FME) i Zoom
Idioma: Anglès.

Títol: Splitting of separatrices in generalized standard maps.

Resum: We study transversal intersections between the invariant manifolds (stable and unstable) associated to an hyperbolic fixed point for a class of maps. These intersections are known as homoclinic orbits. The existence of these kind of orbits is one of the most celebrated methods
to prove the existence of chaotic dynamics in a system. Indeed the Morse-Smale theorem ensures that if there exist transversal intersections between the invariant manifolds of the same invariant object, the system is locally conjugate to a Smale horseshoe with infinite symbols. We look for this phenomena in the named generalized standard maps. This generalization includes the already studied maps like the standard map, first studied by Lazutkin, or the perturbed McMillan map. We obtain an asymptotic formula for the Lazutkin invariant, value related to the area between two homoclinic points, and its first term depends on a Stokes constant that is generically different from zero. To do so, one of the techniques that we use is the inner equation related to our generalized standard maps.


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SIMBa: Moduli spaces of stable vector bundles

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Dimecres 28 de febrer se rcelebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant: Irene Macías Tarrío.
Universitat / Institut de recerca: Universitat de Barcelona.

Data: Dimecres, 28 de febrer de 2024.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: UB (aula B3) and Zoom.
Idioma: Anglès.

Títol: Moduli spaces of stable vector bundles.

Resum: Moduli spaces are essential constructions that arise in connection with classification problems. When dealing with vector bundles on a smooth algebraic variety X, the moduli space of stable vector bundles parametrizes isomorphic classes of stable vector bundles. This talk will
start with the definition and construction of this moduli space from the point of view of algebraic geometry. After this there will be an overview of the Brill-Noether Theory, which concerns the study of certain subvarieties of this moduli space in order to know more about its geometry.


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SIMBa: Subcritical uncertainty principles for the Fourier transform

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Dimecres 14 de febrer se rcelebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant: Miquel Saucedo.
Universitat / Institut de recerca: Centre de Recerca Matemàtica.

Data: Dimecres, 14 de febrer de 2024.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: UAB (CRM aula petita) and Zoom.
Idioma: Anglès.

Títol: Subcritical uncertainty principles for the Fourier transform.

Resum: In this talk I will discuss a type of “relaxed” uncertainty principle for the Fourier transform which has applications in the study of the Schrödinger equation. The main tools are polynomial approximation inequalities.


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SIMBa: Coding theory: into the quantum world

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Dimecres 10 de gener se celebrarcelebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant: Robin Simoens.
Universitat: Universitat Politècnica de Catalunya.

Data: Dimecres, 10 de gener de 2024.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: UPC (FME aula 005) and Zoom.
Idioma: Anglès.

Títol: Coding theory: into the quantum world.

Resum: Classical error-correcting codes were introduced in 1950 by Richard Hamming and are now well-developed. They are built upon the idea of adding redundant information to protect against errors. In 1995, Peter Shor showed that this idea can be carried into the quantum world, giving rise to quantum error-correcting codes, which play a central role in the realization of quantum computers. In this talk, I will give an introduction to both classical and quantum codes, pointing out their differences and similarities.


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SIMBa: Cohomogeneity one – From PDEs to groups and ODEs

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Dimecres 20 de desembre se celebrarcelebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant: Enric Solé Farré.
Universitat: Imperial College London – University College London.

Data: Dimecres, 20 de desembre de 2023.
Hora: 11:40, pausa pel cafè; 11:00, xerrada.
Lloc: UB (FMI aula B1) and Zoom.
Idioma: Anglès.

Títol: Cohomogeneity one – From PDEs to groups and ODEs.

Resum: One of the main problems in differential geometry is solving PDEs involving different geometric quantities. Solutions to most of these PDEs are hard to come by, and one is often forced to reduce to very symmetric scenarios to find examples of solutions. I will first revise some instances of the case with maximal symmetry: homogeneous space; before moving to the cohomogeneity one case. The driving PDE examples will be the Einstein equation and the exceptional holonomy conditons.


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SIMBa: An interior regularity result for the MEMS problem

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Dimecres 29 de novembre se celebrarcelebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant: Renzo Bruera Méndez.
Universitat: Universitat Politècnica de Catalunya.

Data: Dimecres, 29 de novembre de 2023.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: UPC i Zoom.
Idioma: Anglès.

Títol: An interior regularity result for the MEMS problem.

Resum: In this talk we present an interior regularity result for the class of stable solutions to a semilinear elliptic equation with a singular nonlinearity.
The class of nonlinearities that we consider are real-valued functions defined on [0,1) which are positive, nondecreasing, and whose integral on [0,1) is infinite. This equation is a generalization of a model for the deflection of a dielectric elastic membrane in a microelectromechanical system (MEMS). Solutions to this equation are critical points of an associated energy functional. We say that a solution is stable when the second variation of the energy at the solution is nonnegative. Under a growth assumption on the nonlinearity, we are able to prove that every stable solution is regular up to the optimal dimension, n=6.


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SIMBa: Fundamental domains for the Bruhat-Tits tree for $\mathrm{GL}2\left(F{\mathfrak{p}}\right)$

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Dimecres 8 de novembre se celebrarcelebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant: Eloi Torrents Juste.
Universitat: Universitat Autònoma de Barcelona.

Data: Dimecres, 8 de novembre de 2023.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: UAB (aula petita CRM) i Zoom.
Idioma: Anglès.

Títol: Fundamental domains for the Bruhat-Tits tree for \mathrm{GL}_2\left(F_{\mathfrak{p}}\right).

Resum: The computation of fundamental domains of the Bruhat-Tits tree by the action of quaternionic groups allows the computation of harmonic cocycles on it. These are related to automorphic forms and from this fact are derived several applications, as for example the computation of points on Shimura curves and Heegner points on elliptic curves as done by M. Greenberg and later generalized by C. Franc and M. Masdeu.
In this talk we will review these concepts, and we will explain how to apply them in the computation of Heegner points on elliptic curves in cases where the Heegner hypothesis is not satisfied, and therefore the classical arquimedian construction of these points is difficult to compute.