Quasi-modularity of Hodge cycles-清华大学求真书院

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Quasi-modularity of Hodge cycles

来源： 03-24

时间：21:30-22:30, Mar. 24, 2023

地点：Zoom: 559 700 6085（PW: BIMSA）

组织者：Hossein Movasati

主讲人：François Greer (Michigan State University, USA)

Abstract

Period spaces contain Hodge cycles, whose cohomology classes form the coefficients of certain modular forms, by work of Kudla and Millson. I will explain how this phenomenon survives when we pass to a toroidal compactification in the case of K3 type Hodge structures, and then give some geometric applications. This work is joint with Phil Engel and Salim Tayou.

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A symplectic analogy of Hodge theory I
AbstractIn analogous to the Hodge theory, Tsai, Tseng and Yau constructed a novel cochain complex on symplectic manifolds, based on the Lefschetz decomposion. Its cohomology is closely related to the de Rham cohomology, but also carries the information of the symplectic form. In the talk we will go through the definition and properties of this cochain complex
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Leaf schemes and Hodge loci
IntroductionHodge conjecture is one of the millennium conjectures for which the evidences are not so much: It is proved for surfaces (Lefschetz (1,1) theorem) and surface type varieties (like cubic fourfolds), and we do not know even it is true for all Fermat varieties (despite some partial result by T. Shioda and his coauthors). The main goal of the course is introduce computational methods fo...
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书院学术

Quasi-modularity of Hodge cycles

A symplectic analogy of Hodge theory I

Leaf schemes and Hodge loci

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