Algebraic Geometry Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Algebraic Geometry Group-Department of Mathematics
- Location
- 207 Psychology Building
- Date
- Dec 2, 2025 3:00 pm
- Speaker
- Sheldon Katz (University of Illinois Urbana-Champaign)
- Views
- 2
- Originating Calendar
- Algebraic Geometry Calendar
Title: On Gopakumar-Vafa Invariants
Abstract: The integer-valued Gopakumar-Vafa invariants of Calabi-Yau threefolds X were introduced in 1998 in the physics literature. The GV invariants can be recursively defined from the Gromov-Witten invariants as numbers which are a priori only rational, but Ionel and Parker proved in 2017 that these numbers are always integers. However, a rigorous direct mathematical definition of the GV invariants along the lines envisioned by Gopakumar and Vafa is still not quite complete. After surveying the foundational results and conjectures, I discuss recent joint work with Huang and Klemm in the physics literature which gives new (conjectural) methods for determining infinitely many GV invariants at once. The predicted GV invariants are consistent with all mathematical checks which have been performed to date.