Description:

The main goal of the present course is two-folded. First, we develop the theory of Calabi-Yau modular forms introduced in [Mov22b, Mov17a, AMSY16]. Second, we aim to gather the literature on arithmetic modularity beyond elliptic curves, and in particular, rigid Calabi-Yau varieties. For this we will follows [Yui13] and the references therein.

Prerequisite: Algebraic Geometry, Number theory

Reference:

[AMSY16] M. Alim, H. Movasati, E. Scheidegger, and S.-T. Yau. Gauss-Manin connection in disguise: Calabi-Yau threefolds. Comm. Math. Phys., 334(3):889–914, 2016. 

[Mov22b] H. Movasati. Modular and automorphic forms & beyond, volume 9 of Monogr. Number Theory. Singapore: World Scientific, 2022.

[Mov17a] H. Movasati. Gauss-Manin connection in disguise: Calabi-Yau modular forms. Surveys of Modern Mathematics, Int. Press, Boston., 2017. 

[Yui13] N. Yui. Modularity of Calabi-Yau varieties: 2011 and beyond. In Arithmetic and geometry of K3 surfaces and Calabi-Yau threefolds, volume 67 of Fields Inst. Com-mun., pages 101–139. Springer, New York, 2013.

Target Audience: Graduate students

Teaching Language: English

Bio: Hossein Movasati is an Iranian-Brazilian mathematician who since 2006 has worked at the Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro. He began his mathematical career working on holomorphic foliations and differential equations on complex manifolds, and gradually moved to study Hodge theory and modular forms and the role of these in mathematical physics, and in particular mirror symmetry.

Registration: https://www.wjx.top/vm/Oks2Th3.aspx#