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Séminaire de Systèmes Dynamiques
# Clemens’ conjecture

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Europe/Paris

207 (Bâtiment 1R2)
### 207

#### Bâtiment 1R2

Description

Clemens’ conjecture states that the number of rational curves in a generic quintic threefold is finite. In this talk I will give an overview of this conjecture and in particular its relation to Gromov-Witten invariants and String theory. If time allows, I will talk about my recent article arXiv:2202.08677, in which I prove that if it is false then certain periods of rational curves in such a quintic threefold must vanish. The method is based on a generalization of a proof of Max Noether’s theorem using infinitesimal variation of Hodge structures and its reformulation in terms of integrals and Gauss-Manin connection.