José Ignacio Yáñez. PUC Pares Log Canonical y Teorema del Cono Sala 2 PUC
2017-03-31 14:30hrs.
José Ignacio Yáñez. PUC Introducción al Minimal Model Program Sala 2 Abstract: Este semestre estudiaremos el Minimal Model Program (o teoría de Mori) para superficies algebraicas con borde. El objetivo principal es entender la demostración del teorema de boundedness dada por Alexeev a comienzos de los 90s. Este teorema implica que la compactificación del espacio de moduli de superficies algebraicas de tipo general, dada por Kollár y Shepherd-Barron y generalización de la compactificación de Deligne-Mumford para curvas, define una variedad proyectiva. En particular, las singularidades de las correspondientes superficies están acotadas a través de los números de Chern (de hecho K^2 basta), formando una lista finita. ¿Cuál es esa lista para K^2 dado?
La idea es desarrollar todos los prerequicitos para poder entender los detalles de la demostración.
En esta charla se definirán superficies con bordes, las singularidades involucradas junto a sus discrepancias, el teorema del cono, y todo aspecto básico relacionado con MMP.
2017-03-24 14:30hrs.
Fabien Trihan. U Sophia, Japón Abelian varieties over function fields and related conjecture sala 2 Abstract:
We will talk about abelian varieties over function fields of positive characteristic and conjectures related to those such as the Birch-Swinnerton-Dyer, the equivariant Tamagawa number conjecture or the Iwasawa Main conjectures
2017-03-10 16:00hrs.
Dulip Piyaratne. Kavli Ipmu, University of Tokyo Stability conditions on derived categories of varieties II Sala 2 Abstract: In this talk I will discuss stability conditions on projective threefolds. A conjectural construction for any 3-fold was introduced by Bayer, Macri and Toda, and the problem is reduced to proving so-called Bogomolov-Gieseker type inequality holds for certain stable objects in the derived category. It has been shown to hold for some 3-folds including Fano 3-folds of Picard rank one. However, Schmidt and Martinez gave some counter-examples for Fano 3-fold of higher Picard rank. In this talk, I will explain how to modify the original conjectural inequality in order to get a family of Bridgeland stability conditions, and why it holds for general Fano 3-folds.
2017-03-10 15:00hrs.
Dulip Piyaratne. Kavli Ipmu, University of Tokyo Stability conditions on derived categories of varieties Sala 2 Abstract: The aim of this talk is to discuss Bridgeland stability conditions on smooth projective varieties. The notion of stability appears in many guises and it is fundamental to geometric invariant theory. There is a systematic way of studying stability conditions due to Bridgeland and his approach is essentially an abstraction of the usual slope stability for sheaves. This categorical stability notion was introduced in order to understand the work of Douglas on Pi-stability in superconformal field theories. However, construction of Bridgeland stability conditions on higher dimensional varieties is a challenging problem, and from string-theoretic point of view, stability conditions on smooth projective threefolds are the most interesting ones. In this talk, I will recall some important notions associated to derived categories of varieties and stability conditions, with special emphasis on curves and surfaces.
2016-12-01 16:15-17:15hrs.
Sukhendu Mehrotra. PUC Chile The Franchetta Conjecture (Cont.) Fac. de Matematicas, Universidad de Chile
2016-11-24 16:15-17:15hrs.
Sukhendu Mehrotra. Puc, Chile The Franchetta Conjecture Universidad de Chile Abstract:
In 1952, Franchetta made the conjecture any line bundle over the universal curve defined over an open subset of M_g, g>2, restricts to the fibers as a multiple of the canonical bundle. This talk will present a sketch of the proof of Arbarello-Cornalba of this conjecture.
2016-10-20 16:15-17:15hrs.
Anita Rojas. Universidad de Chile Espacio de Teichmüller Fac. de Matemáticas, Universidad de Chile
2016-10-13 16:15-17:15hrs.
Robert Auffarth. Universidad de Chile M_G Como Espacio Analítico Fac. de Matemáticas, U. de Chile
2016-10-06 16:15-17:15hrs.
Víctor González. Utfsm Un Pincel de Curvas Estables Fac. de Matemáticas, Universidad de Chile
2016-10-03 10:30hrs.
Cristián Ortiz. Universidad de Sao Paulo, Brasil Vector bundles over differentiable stacks Sala 2 (Edf. Rolando Chuaquí) Abstract: Stacks are generalized spaces arising in the study of moduli problems. In this seminar we will be mainly concerned with differentiable stacks. Roughly speaking, a differentiable stack is a generalized notion of quotient of a differentiable manifold, which includes orbifolds as special instances. There is a very fruitful interaction between differentiable stacks and the theory of Lie groupoids, namely, isomorphism classes of differentiable stacks are in one to one correspondence with Morita equivalence classes of Lie groupoids. In this talk, we will introduce the notion of Morita equivalence of vector bundles over Lie groupoids, we will explain in which sense this offers a notion of vector bundle in the category of differentiable stacks. Examples will be presented and, if time permits, we will briefly discuss connections with representation theory and symplectic geometry.
2016-09-29 16:15-17:15hrs.
Robert Auffarth. Universidad de Chile Curvas Estables Fac. de Mat., Universidad de Chile
2016-09-15 16:00hrs.
Sergio Troncoso. PUC Chile Moduli y Esquemas de Hilbert (cont.) Fac. de Matemáticas, Universidad de Chile Abstract: Una indtroducción a los problemas de moduli y esquemas de Hilbert.
2016-09-09 11:00hrs.
Sergio Troncoso. PUC Chile Moduli y Esquemas de Hilbert Facultad de Matemáticas, Universidad de Chile Abstract: Una indtroducción a los problemas de moduli y esquemas de Hilbert.
2016-06-16
Giancarlo Urzúa. P. Universidad Católica de Chile Degeneraciones de Superficies y Sus Modelos Minimales Sala 2 de la Facultad de Matemáticas PUC a las 16:00 Hrs.
2016-05-06
Giancarlo Urzúa. P. Universidad Católica de Chile Seminario Sobre Constantes de Seshadri: de Título: Cotas Para Constantes de Seshadri Sala 2 de la Facultad de Matemáticas a las 14:30 Hrs.
2015-12-02
Bruno Suzuki. Universidad Católica del Norte Cohomology of Weighted Projective Spaces Sala 1 - Facultad de Matemáticas UC
2015-06-26
Aníbal Velozo. Princeton University Topología Simpléctica en Superficies Algebraicas y Horikawa Surfaces Sala 2 Facultad de Matemáticas UC - 14:30 Hrs.
2015-06-19
Robert Auffart. Universidad de Chile Sobre la Construcción de Mumford de Variedades Abelianas Degeneradas Sala 2 Facultad de Matemáticas UC - 14:30 Hrs.
2015-03-27
Sebastián Eterovic. P. Universidad Católica de Chile Buscando Curvas Racionales Cuando K es Negativo II Sala 2 - Facultad de Matemáticas UC - 14:30