Dhruv Ranganthan: Moduli spaces in tropical geometry

Abstract: In the last five years, tropical moduli spaces have substantially increased the range and applicability of these combinatorial methods in algebraic geometry, leading to new results in the theory of linear series, enumerative geometry, and the geometry of classical moduli spaces. I will survey recent developments in our understanding of tropical moduli spaces, outline some of these applications to algebraic geometry, and discuss some open questions and speculations, several of a topological or combinatorial nature, that might open new directions in the subject.