Topic: Counting curves with moduli spaces
Abstract: Enumerative geometry is concerned with answering questions like: “given five points in the plane, how many ellipses pass through all five of them?” These problems have a rich history, including some techniques that were not always mathematically rigorous but still produced the right answers (usually). Mathematicians’ attempts to carefully develop the subject of enumerative geometry have led to many recent advances, and even to some unexpected connections with the physics of string theory. In this talk, I will give a tour of some of the problems, pitfalls, and successes in the history of enumerative geometry.
Emily Clader received her Ph.D. in Mathematics from the University of Michigan in 2014. After completing a postdoctoral fellowship at the ETH in Zurich, Switzerland, she joined the faculty at San Francisco State University as an Assistant Professor in 2016. Her current research is in algebraic geometry and moduli spaces.