Speaker：
Lutian Zhao (Kavli IPMU, University of Tokyo)
Time:
November 4, 2026, 2:00–3:00 pm
Venue:
HIMIS 7A1
Title:
What is Gopakumar-Vafa invariant
Abstract:
Gopakumar–Vafa invariants are integer-valued curve-counting invariants of Calabi–Yau threefolds. In this talk, I will introduce their geometric interpretation through moduli spaces of sheaves and their relation to Pandharipande–Thomas stable pairs. Starting with a smooth curve, I will explain how its symmetric powers and Jacobian are related by the classical Macdonald formula, providing a simple model for this correspondence. I will then discuss what changes when singular curves appear and briefly introduce recent results for local projective planes and quadrics. The talk will focus on basic constructions and examples.
Biography:
Lutian Zhao is currently a postdoctoral researcher at the Kavli Institute for the Physics and Mathematics of the Universe (IPMU). He completed his PhD in Mathematics at the University of Illinois Urbana-Champaign (UIUC) under the supervision of Professor Sheldon Katz. His research lies at the intersection of algebraic geometry, representation theory, and theoretical physics.