## Salomon Bochner Lectures in Mathematics, 2007-2008

**Rice University**

Department of Mathematics

# Davesh Maulik

Columbia University/Clay Mathematics Institute

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February 25 - February 28, 2008

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Gromov-Witten theory and Noether-Lefschetz theory for K3 surfaces

In this series of lectures, we discuss two theories concerning families of K3 surfaces (a special class of algebraic surface with trivial canonical bundle).
Gromov-Witten theory involves counting pseudoholomorphic curves on a symplectic manifold and is closely related to ideas from mirror symmetry and hypergeometric
series. Noether-Lefschetz theory, on the other hand, arises from classical geometric questions of Hodge theory but relates to modern work of Borcherds on automorphic
products. In these talks, I will introduce these circles of ideas and explain the precise quantitative relationship between them along with applications to each
side.

Monday, February 25

4:00 - 5:00 PM Keck 100 (Lecture Hall)

Lecture 1.

Tuesday, February 26

4:00 - 5:00 PM Herman Brown 227

Lecture 2.

Thursday, February 28

4:00 - 5:00 PM Herman Brown 227

Lecture 3.

There will be a tea preceding each lecture
in the Mathematics Commons Room, Herman Brown 438.

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