Algebra/Topology Seminar

Speaker: Felix Janda (University of Michigan)

Title: Enumerative geometry: old and new.

Abstract: For as long as people have studied geometry, they have counted
geometric objects. For example, Euclid's Elements starts with the
postulate that there is exactly one line passing through two distinct
points in the plane. Since then, the kinds of counting problems we are
able to pose and to answer has grown. Today enumerative geometry is a
rich subject with connections to many fields, including combinatorics,
physics, representation theory, number theory and integrable systems.

In this talk, I will show how to solve several classical counting
questions. Then I will describe a more modern problem with roots in
string theory which has been the subject of intense study for the last
two decades, namely the study of the Gromov-Witten invariants of the
quintic threefold, a Calabi-Yau manifold. I will explain a recent
break-through in understanding the higher genus invariants that stems
from a seemingly unrelated problem related to the study of holomorphic
differentials on Riemann surfaces.