Back to Departmental Colloquium: Fall 2020
Departmental Colloquium
Date: Thursday, Dec 3, 2020
Time: 4:00PM
Location: JWB 335
Kirsten Wickelgren
Duke University
Title |
An arithmetic count of rational plane curves |
Abstract |
There is a unique line through 2 points in the plane, and a unique conic through 5. These counts generalize to a count of degree d rational curves in the plane passing through 3d-1 points. Surprisingly, the problem of determining these numbers turns out to be deep and connected to string theory, and it was not until the 1990’s that Kontsevich determined them with a recursive formula. Such formulas are valid when you allow your curves to be defined with complex coefficients. For fields of characteristic not 2 or 3, we use A1-homotopy theory to show that by counting with bilinear forms, there is an invariant arithmetic count of rational plane curves. This is joint work with Jesse Kass, Marc Levine, and Jake Solomon. |
Number Theory
Commutative Algebra