Seminario de Geometría Algebraica

Seminario de Geometría Algebraica
2017-08-28
TBAhrs.
Mikhail Borovoi. Tel Aviv University
Cayley Groups
TBA
Abstract:
I will start the talk with the definition of the special orthogonal group SO(n) and with the classical "Cayley transform" for SO(n) constructed by Arthur Cayley in 1846. A connected linear algebraic group G over C is called a *Cayley group* if it admits a *Cayley map*, that is, a G-equivariant birational isomorphism between the group variety G and its Lie algebra Lie(G). For example, SO(n) is a Cayley group.  A linear algebraic group G is called *stably Cayley* if G x (C^*)^r is Cayley for some natural number r. I will consider semisimple algebraic groups, in particular, simple algebraic groups. I will describe classification of Cayley simple groups and of stably Cayley semisimple groups. (Based on joint works with Boris Kunyavskii and others.)
2017-08-25
16:00hrs.
Nicolás Arancibia Robert. Carleton University
Una Introducción al Principio de Funtorialidad de Langlands y a la Conjetura Local de Arthur
Facultad de Matemáticas, sala 2
Abstract:
El objetivo de esta charla es dar una introducción a ciertos aspectos del programa de Langlands. Comenzaremos introduciendo ciertos conceptos necesarios para poder enunciar el principio de funtorialidad para luego dar paso al trabajo de James Arthur sobre la clasificación del espectro automorfo discreto de grupos clásicos. Si el tiempo lo permite, daremos una corta introducción al trabajo de J. Adams, D. Barbasch y D. Vogan sobre la descripción a partir de herramientas geométricas de los llamados paquetes d'Arthur.
2017-08-25
14:30hrs.
Giancarlo Urzúa. PUC Chile
Elementos de Superficies Algebraicas
sala 2
2017-08-18
14:30hrs.
Sergio Troncoso. PUC Chile
Introducción a Las Nociones Básicas en Geometría de Superficies
Sala 2
2017-08-04
14:30hrs.
Natalia García Fritz. PUC Chile
Puntos Racionales y Problemas Diofantinos
sala 2
2017-07-21
15:40-17:00hrs.
Paolo Stellari. Universidad de Milan
Cubic Threefolds And Fourfolds: Geometry And Homological Algebra III
Sala 1
Abstract:
We revisit some classical results concerning the geometry of smooth cubic hypersurfaces of dimension 3 and 4 by means of modern techniques involving derived categories and Bridgeland stability conditions. The examples we want to examine are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds.
https://raizdepie.wixsite.com/algebraic-geometry
2017-07-21
14:00-15:20hrs.
Marcello Bernardara. Universidad de Toulose
Derived Categories, Cycles, And Rationality
Sala 1
Abstract:
In the last decades, semiorthogonal decompositions of derived categories of coherent sheaves have been considered as a possible tool to attack birationality questions. Since the seminal work of Bondal and Orlov, the work of many authors, Kuznetsov above all of them, has made clear what we should expect and which are the main technical problems. In particular, one would expect that the derived category of a rational variety must be decomposed in "codimension 2" subcategories.

The aim of these lectures is to set definitions and property that could give a sense to the above considerations, and to show that this conjectural obstruction is stronger than the known classical ones in cases such as surfaces or Fano threefolds, and closely related for some particular fourfold (cubic, Gushel'-Mukai). A particular attention will be put on constructions related to cycles and motives, such as intermediate Jacobians and decomposition of the diagonal.
https://raizdepie.wixsite.com/algebraic-geometry
2017-07-20
15:40-17:00hrs.
Paolo Stellari. Universidad de Milan
Cubic Threefolds And Fourfolds: Geometry And Homological Algebra II
Sala 1
Abstract:
We revisit some classical results concerning the geometry of smooth cubic hypersurfaces of dimension 3 and 4 by means of modern techniques involving derived categories and Bridgeland stability conditions. The examples we want to examine are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds.
https://raizdepie.wixsite.com/algebraic-geometry
2017-07-20
14:00-15:20hrs.
Marcello Bernardara. Universidad de Toulose
Derived Categories, Cycles, And Rationality II
Sala 1
Abstract:
In the last decades, semiorthogonal decompositions of derived categories of coherent sheaves have been considered as a possible tool to attack birationality questions. Since the seminal work of Bondal and Orlov, the work of many authors, Kuznetsov above all of them, has made clear what we should expect and which are the main technical problems. In particular, one would expect that the derived category of a rational variety must be decomposed in "codimension 2" subcategories.

The aim of these lectures is to set definitions and property that could give a sense to the above considerations, and to show that this conjectural obstruction is stronger than the known classical ones in cases such as surfaces or Fano threefolds, and closely related for some particular fourfold (cubic, Gushel'-Mukai). A particular attention will be put on constructions related to cycles and motives, such as intermediate Jacobians and decomposition of the diagonal.
https://raizdepie.wixsite.com/algebraic-geometry
2017-07-19
15:40-17:00hrs.
Paolo Stellari. Universidad de Milan
Cubic Threefolds And Fourfolds: Geometry And Homological Algebra I
Sala 1
Abstract:
We revisit some classical results concerning the geometry of smooth cubic hypersurfaces of dimension 3 and 4 by means of modern techniques involving derived categories and Bridgeland stability conditions. The examples we want to examine are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds.g derived categories and Bridgeland stability conditions. The examples we want toWe revisit some classical results concerning the geometry of smooth cubic hypersurfaces of dimension 3 and 4 by means of modern techniques involving derived categories and Bridgeland stability conditions. The examples we want to examine are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds. are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds.
https://raizdepie.wixsite.com/algebraic-geometry
2017-07-19
14:00-15:20hrs.
Marcello Bernardara. Universidad de Toulose
Derived Categories, Cycles, And Rationality I
Sala 1
Abstract:
In the last decades, semiorthogonal decompositions of derived categories of coherent sheaves have been considered as a possible tool to attack birationality questions. Since the seminal work of Bondal and Orlov, the work of many authors, Kuznetsov above all of them, has made clear what we should expect and which are the main technical problems. In particular, one would expect that the derived category of a rational variety must be decomposed in "codimension 2" subcategories.

The aim of these lectures is to set definitions and property that could give a sense to the above considerations, and to show that this conjectural obstruction is stronger than the known classical ones in cases such as surfaces or Fano threefolds, and closely related for some particular fourfold (cubic, Gushel'-Mukai). A particular attention will be put on constructions related to cycles and motives, such as intermediate Jacobians and decomposition of the diagonal.
https://raizdepie.wixsite.com/algebraic-geometry
2017-07-14
14:00-16:00hrs.
Sukhendu Mehrotra. PUC
Introducción a Las Categorías Derivadas en la Geometría Algebraica I-Ii
Sala 2
Abstract:
Estas son charlas preparatorias para los mini-cursos de la próxima semana.
2017-07-04
16:00hrs.
Héctor Pastén. Harvard University
Avances Recientes en la Conjetura Abc
Sala 2, Facultad de Matemáticas
Abstract:
Luego de un breve recuento de los métodos y resultados existentes en relación a la conjetura abc, voy a dar un esbozo una técnica nueva basada en curvas de Shimura y voy a explicar el tipo de resultados incondicionales que permite obtener.
2017-06-16
14:30hrs.
Sukhendu Mehrotra. PUC Chile
Exceptional Bundles From Surface Degenerations II
sala 2
2017-06-09
14:30hrs.
Sukhendu Mehrotra. PUC Chile
Exceptional Bundles From Surface Degenerations I
sala 2
2017-06-02
14:30hrs.
José Yáñez. PUC Chile
Puntos de Acumulación de K^2 en Superficies Estables
sala 2, Facultad de Matemáticas PUC
2017-05-26
14:30hrs.
Sergio Troncoso. PUC Chile
Theory Of Peeling
sala 2
2017-05-19
14:30-16:00hrs.
Sönke Rollenske. U Marburg
Geometry Of Stable Surfaces III
Sala 2, Facultad de Matemática
2017-05-12
16:00 - 17:00hrs.
Sönke Rollenske. U Marburg
Geometry Of Stable Surfaces II
Sala 2, Facultad de Matemáticas
2017-05-12
14:30-15:45hrs.
Sönke Rollenske. U Marburg
Geometry Of Stable Surfaces I
Sala 2, Facultad de Matemáticas
Abstract:
Stable surfaces are the two-dimensional analogue of stable curves: they are
the singular surfaces that are parametrised by a natural compactification of
the Giesecker moduli space of surfaces of general type.
In the lectures I will illustrate some basic techniques needed to deal with
such surfaces. We will see that any closer look at examples quickly takes us
to classical questions in algebraic geometry.