# Geometric Analysis and Topology Seminar

#### 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.