Modular forms and Calabi-Yau varieties


Hossein Movasati

13:30:00 - 15:00:00

R440 , Astronomy and Mathematics Building

Classical modular forms and in general automorphic forms enjoy q-expansions with fruitful applications in different branches of mathematics. From another side we have q-expansions coming from the B-model computations of mirror symmetry which, in general, are believed to be new functions. In this series of talks I will present a common algebro-geometric framework for all these q-expansions. This is based on the moduli of varieties with a fixed topological data and enhanced with a basis of the algebraic de Rham cohomology, compatible with the Hodge filtration and with a constant intersection matrix. In our way, we will also enlarge the algebra of automorphic forms to a bigger algebra which is closed under canonical derivations. I will mainly discuss two examples: 1. Elliptic curves and classical modular forms, 2. Mirror quintic Calabi-Yau varieties, Yukawa coupling and topological partition functions. The talks are based on the following articles available in arxiv: H. Movasati, Modular-type functions attached to mirror quintic Calabi-Yau varieties, H. Movasati, Quasi-modular forms attached to elliptic curves I, Annales Mathématique Blaise Pascal, v. 19, p. 307-377, 2012.