SAG: Hilbert schemes of points, quantum cohomology and tropical curvesSeminar Algebraic Geometry (SAG)

by Qaasim Shafi

Thursday Jan 15, 2026, 10:00 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

For a smooth surface S, the Hilbert scheme of points on S gives a smooth compactification of the configuration space of n distinct points on S. Its cohomology is by now well understood and exhibits deep connections with representation theory. Understanding its quantum cohomology, a deformation of ordinary cohomology involving curve counting invariants, has since received a lot of attention. I'll explain some joint work in progress with Georg Oberdieck and Aaron Pixton about how to determine this ring for an elliptic surface, with the help of tropical geometry.