Enumerative Geometry: Old and New
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 start by demonstrating how to solve a classical counting question. I will then move to a more modern problem with roots in string theory which has been the subject of intense study for the last three decades: The computation of the Gromov-Witten invariants of the quintic threefold, an example of a Calabi-Yau manifold.
Bio: Dr. Janda received his PhD from ETH Zurich in 2015 and is currently an Assistant Professor at the University of Notre Dame.