Coloquio de Matemática UC

El Coloquio de Matemática UC está dirigido a todo la comunidad matemática de la UC y en particular a los estudiantes de pregrado y posgrado, por lo cual se presentan de manera general los temas principales del expositor, con el propósito de motivar a los estudiantes. Esta es una instancia excelente para nuestros estudiantes de posgrado, por ejemplo.

El sitio anterior del coloquio con información sobre charlas anteriores se puede encontrar aquí.

El público se compone de personas que tienen una formación general en matemática. Estamos en particular tratando que los coloquios sean más bien generales, dirigidos principalmente a estudiantes de Matemática. Las charlas duran 50 minutos (mas discusión). Por favor adaptar el nivel de los primeros 25 minutos (por menos) de su presentación a este público. Nosotros consideramos estas sugerencias en el sitio de AMS útiles:

Enno Nagel. (Jussieu)
Fractional Derivatives in P-Adic Analysis
Sala 2 (Víctor Ochsenius)- Facultad de Matemáticas - 14:00 Hrs.
Abstract: Motivated by their appearance in the p-adic Langlands program, I firstly introduce by elementary means, for a real number r>=0, the notion of an r-times differentiable function over a p-adic number field and present their basic properties. If time permits, I will then discuss their role in Number Theory and show how they entered the scene as completions of certain locally algebraic representations.
Alvaro Liendo. Mathematisches Institut, Universitat Bern
The Automorphism Group of a T-Variety of Complexity One
Auditorio Ninoslav Bralic - 16:10 Hrs
A T-variety is a normal variety endowed with a faithful action of the algebraic torus T=(k^*)^n. The complexity of a T-variety is the codimension of a generic orbit. The best known examples of T-varieties are toric varieties, i.e., T-varieties of complexity 0.

In the first part of this talk, we present a combinatorial description of T-varieties given by Almann, Hausen and Süss in 2006. This description generalizes the usual description of toric varieties by means of fans to higher complexity. In the second part of this talk, we will discuss a recent result where we compute the root system of the automorphism group of a rational complete T-variety of complexity one.

Igor Dolgachev. University of Michigan
Automorphism Groups of Algebraic Surfaces
Auditorio Ninoslav de la PUC - 15:00 Hrs.
Abstract: I will survey some recent and old results about automorphism groups of complex algebraic surfaces with special emphasis on rational, Enriques and K3 surfaces
Kazim Buyukboduk. Koc University de Estambul
Zeta-Functions and Arithmetic
Sala 2 (Víctor Ochsenius) - 14:30 Hrs. Facultad de Matemáticas - UC
The purpose of this expository talk is to discuss a fundamental theme in modern Number Theory: The relation between zeta-functions (objects of analytic nature) and certain objects of arithmetic nature (which we generally call Selmer groups). Kummer was first to recognize the arithmetic significance of the special values of the classical zeta-function, using which he was able to deduce a non-trivial portion of the Fermat´s Last Theorem". Kummer´s ideas were much later generalized by Ribet and Wiles (in a certain sense) to conclude with the full proof. An important portion of this talk will be devoted to explaining Kummer´s ideas, and if time permits, say a few words about their influence in modern day number theory.

Jouni Rättyä. Universidad de Joensuu, Finlandia
Ecuaciones Diferenciales Lineales en el Disco: Ceros y Crecimiento
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
John Carter. Seattle University, Washington, Usa
Higher-Order Symplectic Numerical Methods for Pdes
Auditorio Ninoslav Bralic -15:00 Hrs - Facultad de Matemáticas
Abstract: Many classic partial differential equations, such as the nonlinear
Schrödinger equation and the Korteweg–de Vries equation, have underlying
Hamiltonian structure. Preserving this property in numerical
simulations is important, especially for long-time evolution. We will
discuss a method for constructing operator-splitting-based high-order
numerical methods that preserve the Hamiltonian (symplectic) structure.
Further, we will apply these ideas to initial value problems with quasi-periodic boundary conditions.
Eleuterio Toro. University of Trento, Italy
Centred Numerical Schemes for Hyperbolic Equations in Conservation Form.
Auditorio Ninoslav Bralic -15:00 Hrs
Francisco-Javier Sayas. Universidad de Minnesota
Numerical Integral Scattering (Dispersión Numérica de Ondas Por Integrales)
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Yaël Frégier. Institut de Mathématiques, Université Du
Algebraic Structures Derived From Minimal Models
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Yakov Eliashberg. Universidad de Stanford, Usa
Flexible and Rigid Mathematics
Auditorio Ninoslav Bralic -16:30 Hrs
Ricardo Menares. Université Paris Sud
Geometria de Arakelov y Curvas Modulares
Sala D101 - Bachillerato - 16:30 Hrs.