Mirror Symmetry in Enumerative Geometry
Time and place
1 PM on Thursday, November 12th, 2015;
Mark Shoemaker (University of Utah)
Abstract
The goal of enumerative geometry is to study a manifold M by counting the number of subspaces of M satisfying certain conditions. One well known class of examples are Gromov—Witten invariants, which count the number of Riemann surfaces lying in M.
While these types of enumerative problems have been studied in various incarnations for over two centuries, interest in them was revived in the 1990s when a surprising connection was made with string theory. This discovery led to a new understanding of the structure of these invariants - one which had previously been unknown to mathematicians. In this talk I will describe some of the mathematical implications of this connection between enumerative geometry and physics, and explain how it has been employed both to answer longstanding questions and to generate new conjectures.
