Colloquium: Tropical geometry and curve counting

Abstract: The goal of this colloquium is to introduce a circle of ideas and techniques used to deal with enumerative geometric problems of curves, concerned with finding the number of curves of a certain type that satisfy a certain number of geometric conditions. We will use as a motivating example the question of double Hurwitz numbers, which enumerate ramified covers of the projective line with prescribed profiles over 0 and infinity.  Tropical geometry provides on the one hand a combinatorial framework to compute Hurwitz numbers in terms of a sum of weighted graphs, and on the other it connects these enumerative invariants to the tautological intersection theory of the logarithmic DR cycle in the moduli space of curves. This perspective opens up a path to new enumerative geometric problems whose solutions exhibit interesting algebraic combinatorial structure. 

Host: Carl Lian

Reception to follow at Cupples I, Room 200 (Lounge) from 2:00pm to 3:00pm