Motivated by classical enumerative geometry and mathematical physics, counting curves in Calabi-Yau 3-folds has been studied intensively for decades, including Gromov-Witten theory and Donaldson-Thomas theory. The physics proposal of Gopakumar-Vafa connects the counting invariants mentioned above to geometry of certain moduli of sheaves. I will discuss recent developments of the Gopakumar-Vafa theory in some examples including Higgs bundles, K3 surfaces, and local P2. In these stories, perverse filtrations play a crucial role, and the Gopakumar-Vafa theory interacts with some other geometric structures and conjectures in a surprising way.
Perverse filtrations and enumerative geometry
04.06.2024 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: