Geometric Analysis and Topology Seminar

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Counting Curves in Calabi-Yau 3-Folds

Speaker: Richard Thomas, Imperial & Columbia

Location: Warren Weaver Hall 813

Date: Tuesday, May 1, 2007, 11 a.m.

Synopsis:

There are many ways to count holomorphic curves in complex manifolds. The famous MNOP conjecture relates 2 of them – Gromov-Witten theory, which counts maps to the manifold (or parametrised curves), and sheaf theory, which counts embedded one-dimensional subschemes (or unparametrised curves). I will review this, and describe one slightly unpleasant aspect in the sheaf theory which means we have to count zero dimensional subschemes (points!) too. Finally I will describe a third way to count unparametrised curves that is joint work with Rahul Pandharipande, which resolves this unpleasantness.

Notes:

Rescheduled from Friday, April 27, 2007.