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Facultad de Matemáticas - PUC, Chile

La Facultad de Matemáticas de la Pontificia Universidad Católica invita a profesores y estudiantes a participar de una serie de mini-cursos que se realizarán entre los días 19 y 21 de julio del año 2017.

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En esta serie de mini-cursos se discutirá el uso de técnicas derivadas en la geometría algebraica clásica. Investigadores internacionales estarán a cargo de las charlas.

 

El primer curso estará a cargo del profesor del departamento de Matemáticas de la Universidad de Milan, Paolo Stellari, quien hablará sobre la geometría de los cúbicos. El segundo curso o dictará el profesor de la Universidad de Toulose, Marcello Bernardara. Sus mini-cursos estaran relacionados a los nuevos métodos derivados en el estudio de cuestiones de racionalidad.

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Todos los mini-cursos se llevarán a cabo en la Sala 1 de la Facultad de Matemáticas de la Pontificia Universidad Católica. La programación de éstos es la siguiente:

Derived techniques in classical

algebraic geometry

19-21 Julio 2017

La información de las charlas que dictarán los profesores Stellari y Bernardara se detallan a continuación:

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Expositor: Paolo Stellari

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Título: Cubic threefolds and fourfolds: geometry and homological algebra

Resumen:
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.

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Expositor: Marcello Bernardara

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Título: Derived categories, cycles, and rationality.

Resumen: 

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.

FACULTAD DE MATEMATICAS

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PONTIFICIA UNIVERSIDAD

CATOLICA DE CHILE

Para mayor información acerca de los mini-cursos y la programación de éstos, contactarse con el profesor Sukhendu Mehrotra  al correo smehrotra@mat.uc.cl.

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