3/21- Shelby Cox: Counting Curves in the Plane

We are very happy to restart the math club with the talk given by Shelby Cox, our own undergraduate student, after the spring break. Please see the abstract below.


Counting Curves in the Plane

Curve counting goes all the way back to Euclid, who asked how many lines pass through 2 given points in the plane. More generally, we can ask how many curves of degree d pass through 3d-1 points. In this talk, I will present a beautiful and well-known proof for the case when d=3, which uses methods from Topology, Geometry, and Algebraic Geometry. The talk will focus on introducing concepts like the Euler characteristic, projective space, and blow-ups, which can help us answer long-standing questions, like: how many pentagons are on a soccer ball? In particular, the talk should be accessible to most math majors.