Noticimat 22

Resumen: In this presentation, we will discuss existence and uniqueness of the solutions of stochastic differential equations, topic motivated by its numerous applications in biology or finance for instance. Firstly, we will review what are the results obtained since the paper of Yamada and Watanabe, published in 1970, in which they state their famous theorem on the uniqueness of solutions. More recently a multidimensional and matrix analogous has emerged with a proof requiring the study of non colliding systems of particles. The latter is studied more in depth by Graczyk and Malecki with the idea of introducing symmetric polynomials. Afterwards, we shall focus on fractional Brownian motion: see some of its properties and raise the issue of stochastic integration with respect to this process. We will finish explaining some of the matters related to existence and uniqueness of the solutions of matrix stochastic differential equations driven by fractional Brownian motion.

Resumen: Alexandrov spaces (with curvature bounded below) are metric generalizations of complete Riemannian manifolds with a uniform lower sectional curvature bound. Instances of Alexandrov spaces include compact Riemannian orbifolds and orbit spaces of isometric compact Lie group actions on compact Riemannian manifolds. In addition to being objects of intrinsic interest, Alexandrov spaces play an important role in Riemannian geometry, for example, in Perelman's proof of the Poincaré Conjecture. In this talk I will discuss the topology and geometry of 3-dimensional Alexandrov spaces, focusing on their classification under certain geometric constraints (for example, positive curvature).

Resumen: We establish a bijection between non-commutative stochastic processes with monotone independent increments, some class of Markov processes and some class of Loewner chains. This is a joint work with Uwe Franz and Sebastian Schleissinger.

Luis Islas Cruz, quien el pasado viernes 7 de junio obtuvo el título de Licenciado en Matemáticas con la presentación y defensa de su tesis Espacios de Funcionales Aditivos y Espacios Duales de BM (Σ) y L∞(μ), dirigida por el Dr. Fernando Galaz Fontes (CIMAT). El jurado estuvo integrado por el Dr. Fernando Núñez Medina (UG), Presidente; la Dra. Berta Gamboa de Buen (CIMAT), secretaria; y la Dra. Celia Ávalos Ramos (UdeG), vocal.

Javier Vázquez Camacho, quien el pasado lunes obtuvo el grado de Maestro en Ciencias con Especialidad en Probabilidad y Estadística con la presentación y defensa de la tesis titulada Análisis del Modelo de Lévy de Riesgo con Cambio de Régimen Basado en el Declive. Los integrantes del jurado fueron la Dra. Ekaterina Todorova Kolkovska (CIMAT), presidenta; Dr. Ehyter Matías Martín González (UG), secretario; y el Dr. José Luis Ángel Pérez Garmendia (CIMAT), vocal y director de la tesis.

Jurgen Alfredo Julio Batalla, quien también este viernes 14 obtuvo el grado de Doctor en Ciencias con Orientación en Matemáticas Básicas, con la presentación y defensa de su tesis Topological and Geometric Aspects of Yamabe-Type Equations. El jurado estuvo integrado por el Dr. Raúl Quiroga Barranco (CIMAT), presidente; el Dr. Gil Bor (CIMAT), secretario; el Dr. Héctor Andrés Chang Lara (CIMAT), vocal; el Dr. Pierre Michel Bayard (UNAM), vocal; y el Dr. Jimmy Petean Humen (CIMAT), vocal y director de la tesis.