Enumerative geometry of curves via tautological classes

Abstract: Enumerative geometry has been at the heart of geometry for more than two millennia. Its aim is to answer questions of the following kind: how many geometric objects $X$ there are satisfying conditions $Y_1,\ldots,Y_n$. In this talk, I will begin with a brief history of enumerative geometry before discussing modern tools for addressing such questions. In particular, I will introduce moduli spaces, their intersection theory, and tautological classes. I will then use these notions to present joint work with Adrien Sauvaget and David Holmes on the enumerative geometry of stable curves.

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar