Algebra and Geometry Seminar

USC Kaprelian Hall room 414

Modular forms are certain kinds of generating functions with nice finite-dimensionality properties that allow you to prove combinatorial identities by checking finitely many cases. Famously, they have been used to solve many problems in number theory and arithmetic geometry. More recently, highly nifty results of Borcherds and Kudla-Milson have led to applications of modular forms to enumerative problems in (complex) algebraic geometry as well. In this talk, I will give an overview of some of these ideas, and describe a particular application of them to a problem about rational elliptic surfaces in joint work with François Greer and John Sheridan.