# Algebraic Geometry Seminar

#### Counting Curves in 3-Folds and 5-Folds

**Speaker:**
Andrei Okounkov, Columbia University

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, December 3, 2013, 3:30 p.m.

**Synopsis:**

There are many ways to count curves of given degree and genus in threefolds which, conjecturally, are all related by simple functional relations for the corresponding all-genera generating functions. In this talk, I will discuss a rather different conjecture about these functions that relates them to counting curves in certain Calabi-Yau 5-folds. In this way, the genus-counting variable *q* of the generating function becomes an equivariant parameter in extra dimensions. Among other things, this gives a very geometric way to sum up these series into a rational function of *q*. Joint work with Nikita Nekrasov.