Hora: 04:15 PM
Ponente(s): Samuel Lisi (University of Mississippi, http://home.olemiss.edu/~stlisi/)
Titulo: Symplectic capacities: embeddings and dynamics
Resumen: This talk will give an introduction to symplectic capacities, a class of numerical invariants that relate dynamical properties of Hamiltonian systems to the geometry of symplectic manifolds. Symplectic manifolds are the natural setting in which to consider Hamiltonian dynamical systems. Indeed, they very naturally generalize cotangent bundles (phase space). Unlike Riemannian manifolds, symplectic manifolds don't have local invariants. They do, instead, admit invariants that obstruct symplectic embedding. Remarkably, these embedding obstructions and dynamical properties of Hamiltonian systems are intimately connected by means of symplectic capacities. (Most of the talk will be an overview of the field, but I will also discuss some joint work with Antonio Rieser.)
Enlace de transmisión: https://bluejeans.com/815617428

Hora: 04:15 PM
Ponente(s): Ryan Hynd (University of Pennsylvania, https://rhynd.math.upenn.edu/)
Titulo: Sobolev’s and Morrey’s inequality
Resumen: Sobolev's and Morrey's inequalities are two of the most important inequalities for functions of several variables.  I will discuss some of the background and mathematics for each of these inequalities.
Enlace de transmisión: https://bluejeans.com/815617428

Hora: 04:15 PM
Ponente(s): Rubí Rodríguez, Universidad de La Frontera, Temuco, Chile
Titulo: Resultados clásicos y recientes en Moduli de variedades abelianas y curvas.
Resumen: Discutiremos acciones de grupos y álgebras en objetos geométricos como toros complejos, variedades abelianas y curvas.

Hora: 04:15 PM
Ponente(s): Thomas Batard CIMAT, A.C. Guanajuato (https://sites.google.com/site/tomasbatard/home)
Titulo: Local and non local variational models for color image restoration
Resumen:
Enlace de transmisión: https://bluejeans.com/815617428

Hora: 04:15 PM
Ponente(s): Makoto Ozawa, Komazawa University, Tokyo, Japan, (https://www.komazawa-u.ac.jp/~w3c/)
Titulo: Critical complexes
Resumen: We work in the piecewise linear category. Generally, for two connected simplicial complexes $X$ and $Y$, $X$ is said to be {\em critical} for $Y$ if $|X|$ cannot be embedded in $|Y|$, but for any point $p\in |X|$, $|X|-p$ can be embedded in $|Y|$. Let $\Gamma(Y)$ denote the set of critical complexes for $Y$. For example, by Kuratowski's and Wagner's theorems, we have $\Gamma(S^2)=\{K_5,K_{3,3}\}$. First, we characterize $\Gamma(F_g)$, where $F_g$ is a closed orientable surface of genus $g>0$. Next, we characterize the critical complexes for the 3-sphere $S^3$ which have a form $(G\times S^1)\cup H$, where $G$ and $H$ are graphs. Suppose that a complex $X$ cannot be embedded in $S^3$. Then we expect that there is a subspace $X'\subset X$ which is critical. However, there are many complexes which cannot be embedded in $S^3$ but do not contain any critical complexes. From those examples, we introduce an equivalence relation on complexes and revise the definition of critical. This is a joint work with Mario Eudave-Mu\~{n}oz.
Enlace de transmisión: https://bluejeans.com/815617428

Hora: 04:15 PM
Ponente(s): Adriana Hansberg (Instituto de Matemáticas, Universidad Nacional Autónoma de México)
Titulo: La evolución de patrones bicolor
Resumen: El teorema de Ramsey nos dice que, para cualquier entero positivo t y un entero n suficientemente grande, si coloreamos todas las aristas de una gráfica completa de n vértices ya sea de rojo o de azul, inevitablemente se formará una gráfica completa monocromática (solo roja o solo azul) con t vértices. Por otro lado, el Teorema de Turán nos dice que, si una gráfica tiene cierto mínimo número de aristas, entonces ésta contendrá una subgráfica completa con t vértices. Relacionado con estos dos problemas, estudiaremos cómo, dependiendo de la saturación que haya de ambos colores en una coloración de las aristas de la gráfica completa, van emergiendo ciertos patrones bicolor muy particulares.

Hora: 04:15 PM
Ponente(s): Luis Nuñez Betancourt (CIMAT, A.C.)
Titulo: La ecuación funcional para cocientes de polinomios
Resumen: La ecuación funcional surge en la teoría de operadores diferenciales como una forma sistemática de disminuir la potencia de una función polinomial. Esta ecuación se ha usado para obtener varias aplicaciones en distintas áreas, por ejemplo, geometría birracional, teoría de números analítica, álgebra conmutativa y teoría cuántica de campos. En esta charla discutiremos una versión de esta ecuación para funciones dadas por el cociente de dos polinomios. Los resultados de esta charla son trabajo en conjunto con Josep Àlvarez Montaner, Manuel González Villa y Edwin León Cardenal.
Enlace de transmisión: https://bluejeans.com/815617428
Notas: Boletín de Información - Febrero 2023

Hora: 04:15 PM
Ponente(s): Marco Mazzucchelli ( École normale supérieure de Lyon, http://perso.ens-lyon.fr/marco.mazzucchelli/)
Titulo: Surfaces of section for geodesic flows of closed surfaces
Resumen: A surface of section for the flow of a nowhere vanishing vector field on a closed 3-manifold N is a compact surface in N, with interior transverse to the vector field, and boundary tangent to the vector field. A surface of section is global when it intersects any orbit segment of length T, for some T>0. Surfaces of section are objects of great interest in dynamics, as they allow to reduce the study of a 3-dimensional flow to the study of a surface diffeomorphism. In this talk, I will present a few results on surfaces of section for geodesic flows of closed surfaces, culminating with the existence of global surfaces of section for all those geodesic flows satisfying the C-infinity generic Kupka-Smale condition (joint work with Gonzalo Contreras, Gerhard Knieper, and Benjamin Schulz). As an application, I will present a characterization of the Anosov condition, which implies the validity of the C^2-structural stability conjecture for geodesic flows of closed surfaces (joint work with Gonzalo Contreras).
Lugar: Centro de Investigación en Matemáticas De Jalisco s/n Valenciana 36023 Guanajuato, Gto. México Guanajuato México
Enlace de transmisión: https://bluejeans.com/815617428

Hora: 04:15 AM
Ponente(s): Jesús Alfredo Sierra Nuñez (Instituto de Matemáticas, UNAM)
Titulo: Dispersive equations for Bose-Einstein condensates
Resumen: We study the well-posedness of two (nonlinear Schrödinger) systems modeling the non-equilibrium dynamics of pumped decaying Bose-Einstein condensates. In particular, we present the local theory for rough initial data using the Fourier restricted norm method introduced by Bourgain. We extend the result globally for initial data in L^2. Finally, we discuss the smoothing of these systems using Bourgain’s High-Low decomposition and applications of Tao’s I-method for the global theory.
Enlace de transmisión: https://bluejeans.com/815617428

Hora: 04:15 PM
Ponente(s): Sunder Sethuram (University of Arizona, https://www.math.arizona.edu/~sethuram/)
Titulo: Corner growth and traffic on a one lane road
Resumen: In the corner growth model on the first quadrant of Z^2, squares are added/removed according to the rule: Squares in the other quadrants are always `on'. A new `on' square in the first quadrant is added with rate p if there are `on' squares just below and to the left of it. An old `on' square is removed with rate 1-p if there are no `on' squares just above and to the right of it. Such a model may also be written in terms of the simple exclusion process on Z, that is `traffic' in one dimension. Depending on the value of p, different evolutions arise in different scales. In this talk, we review some of the previous developments, and discuss a recent result when p=1/2.