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Wednesday, September 4, 2019

**Abstract:** Curve counting invariants on K3 surfaces turn out to have an interesting connection to modular forms via Yau-Zaslow formula. In this talk, starting from the basic properties of K3 surfaces, I’ll discuss two proofs of Yau-Zaslow formula due to Beauville which uses Euler characteristic of compactified Jacobian, and Bryan-Leung using Gromov-Witten technique. If time permits, I’ll describe generalizations of the formula such as Göttsche’s formula and Katz-Klemm-Vafa formula.