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Seminários do IMPA

Variedades de Calabi-Yau

Título |
Modular and automorphic forms & beyond |

Expositor |
Hossein Movasati
IMPA |

Data |
Terça-feira, 13 de março de 2018, 15:30 |

Local |
Sala 224 |

Resumo |

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.