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Seminários do IMPA

Variedades de Calabi-Yau

Modular and automorphic forms & beyond
Hossein Movasati

Terça-feira, 13 de março de 2018, 15:30
Sala 224

The main aim of this research/reading minicourse is to use the available tools in Algebraic Geometry, such as Geometric Invariant Theory, and construct the moduli space  T of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. It turns out that such moduli spaces are of high dimension  and enjoy certain foliations, called modular foliations,  which are of  high codimension, and are constructed from the  underlying Gauss-Manin connection. The mincourse will be mainly  focused on three independent topics: 1. Hilbert schemes and actions of reductive groups and the construction of the moduli space T.  2. The theory of foliations of arbitrary codimensions on schemes and its relation with Noether-Lefschetz  and Hodge loci in the case of modular foliations. 3. To rewrite available theories of automorphic forms, such as Siegel modular forms, Hilbert modular forms, modular forms for congruence groups, and in general automorphic forms on Hermitian symmetric domains,  using the moduli space T. This  will produce a geometric theory of differential equations of automorphic forms.