Title: From classical to tropical enumerative geometry
Speaker: Renzo Cavalieri (Colorado State University)
Abstract: Enumerative geometry is an ancient branch of mathematics that concerns itself with counting geometric object subject to a set of geometric constrains. We all solved our first enumerative geometric problem when we realized that there is precisely one line passing through two distinct points in the plane. The main goal of this colloquium is to illustrate the point that enumerative geometric questions lead to a lot of interesting mathematical ideas and connections. We will use Hurwitz theory - the study of analytic maps of Riemann Surfaces, as our leading example. In this case the enumerative geometric problem is to count the number of such maps once an appropriate set of discrete invariants is fixed.
Classically this problem is tackled via a translation through a topological and into a representation theoretic question. In recent times, tropical geometry has provided an interesting perspective on this problem, exhibiting a natural connection with the world of integrable hierarchies.
Colloquium URL: https://web.math.osu.edu/colloquium/