Claremont Topology Seminar: Reginald Anderson (Claremont McKenna College)

We especially welcome all undergraduates and graduate students to attend topology seminar!

Speaker: Reginald Anderson (Claremont McKenna College)

Title: Kontsevich’s Recursive Formula for Rational Plane Curves

Abstract: Gromov-Witten theory was developed in the 1990s as a curve-counting theory by integrating cohomology classes against a virtual fundamental class for a moduli space of stable maps. One early success of the theory was Kontsevich’s recursive formula for enumerating the number of rational plane curves through 3d-1 points in general position. Starting from a consideration of which genus 0 Gromov-Witten invariants for the complex projective plane can possibly be non-zero, we will assemble a generating function for these invariants, called the genus 0 Gromov-Witten potential for the complex projective plane. If time allows, we will also use the fact that the potential satisfies a partial differential equation called the Witten-Dijkgraaf-Verlinde-Verlinde equation to solve for N_d, the coefficients of the generating function, which give the number of rational plane curves through 3d-1 points.

This talk follows p. 24-26 of these notes, available at https://arxiv.org/abs/2501.03232.

All are welcome.