Archivos mensuales: julio 2015

Agosto

Miércoles 5 de agosto, 14:30-16:40. Sala 2-3 IMA-PUCV

Expositor: Jean Gillibert (U. de Toulouse 2)

Título: Picard groups and class groups

Resumen : Given a smooth projective variety dened over Q and a point of V dened over a number eld K, there exists a naive way to specialize the Picard group of V in the class group of K. Moreover,one is able to control the specialization of torsion divisor classes. This gives an approach to constructing number elds whose class group hasa large F_p rank.
There is an analogous problem where class groups are replaced by Selmer groups of elliptic curves. We brie y explain how these two problems are related.
Part of this work is in collaboration with Aaron Levin and Yuri Bilu.


Miércoles 19 de agosto, 14:30-16:40.   Sala 8, Facultad de Ciencias, U. de Valparaíso

Expositor: Pedro Montero (U. de Grenoble)

Título: Sobre el número de Picard de variedades de Fano singulares

Resumen :

El Programa de Modelos Minimales o MMP (por “Minimal Model Program”) busca extender la teoría de modelos minimales de superfices algebraicas lisas a dimensiones superiores. Una de las primeras y más importantes diferencias respecto al caso de superficies es la existencia de variedades algebraicas proyectivas lisas que no admiten modelos minimales lisos. Por lo tanto, debemos estudiar variedades con ciertas singularidades para poder extender la teoría a dimensiones superiores.

Durante la primera parte de la charla discutiremos sobre los resultados fundamentales de esta teoría tales como el teorema del cono de Mori, e ilustraremos, en el caso tórico, como cada paso del MMP se traduce de manera combinatoria.

Durante la segunda parte discutiremos resultados recientes sobre la clasificación de variedades de Fano que admiten un divisor con numero de Picard 1. Veremos que la existencia de tal divisor tiene implicancias en la geometría birracional de la variedad. Comentaremos los resultados en el caso que la variedad de Fano es supuesta lisa, y discutiremos sobre como extenderlos al caso singular.


Miércoles 26 de agosto, 14:30-16:40. Sala 8, Facultad de Ciencias, U. de Valparaíso

Expositora: Mariela Carvacho (UTFSM)

Título: Some aspect on the classication of group actions on compact Riemann surfaces

Resumen :When we consider a group G and say that G acts on a Riemann surface S, we are saying that there exists a group monomorphism from G to Aut(S), where Aut(S) is the group consisting of the self-maps of S (automorphism) which preserve the complex structure. In the study of Riemann surfaces, the classication of actions on compact Riemann surfaces is an interesting problem. The purpose of this talk is to give a general vision of this problem and
the main tools that are used to study it. Finally we show some recent results about this subject.

Julio

Miércoles 22 de Julio, 14:30-16:40. IMA-PUCV

Expositor: Anne-Marie Aubert (Institut de Mathematique de Jussieu)

Título: Conjectures on representations of p-adic groups in relation
with the local Langlands correspondence

Resumen : We will present several conjectures about complex repre-
sentations of p-adic reductive groups in relation with the local Lang-
lands correspondence.
On the representation side we will consider an arbitrary Bernstein
component in the space of irreducible smooth representations of the p-
adic group and describe a conjectural simple description of it in terms
of a twisted extended quotient of the associated Bernstein torus with
respect to the associated nite group. That is is possible is explained
by the expected shape of the Hecke algebra associated to the Benstein
component. These conjectures have been proved for principal series
representations of split groups, for inner forms of the general linear
group and for inner forms of the special linear group. It is joint work
with Paul Baum, Roger Plymen and Maarten Solleveld.
Next we will describe a Galois analog, due to Ahmed Moussaoui, of
the above description, in which the role of the Bernstein component is
played by a certain subset of the set of enhanced Langlands parame-
ters. It involves in particular a conjectural geometric parametrization
of the supercuspidal representations, which is proved for symplectic
and orthogonal groups.