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Mathematics Colloquium


Date:  Tuesday, October 12, 2010

Title:  Enumerative geometry of K3 surfaces

Abstract:  In this lecture, we discuss enumerative invariants for families of K3 surfaces (a special class of algebraic surface with trivial canonical bundle). The first example - Noether-Lefschetz invariants - arise from classical geometric questions about holomorphic line bundles on these surfaces and how they vary in families. Gromov-Witten theory, on the other hand, involves counting pseudoholomorphic curves on a symplectic manifold and is closely related to ideas from mirror symmetry and hypergeometric series. In this talk, I will try to introduce these circles of ideas and how they're related. If time permits, I'll discuss conjectural generalizations to other types of surfaces.

Speaker:  Davesh Maulik
Institution:  Clay Fellow


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