Concrete models for atoms and a Chen-Ruan toy model
Organizers
Speaker
Leonardo F. Cavenaghi
Time
Thursday, September 19, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
In recent years, built upon mirror symmetry reasoning, Katzarkov, Kontsevich, Pantev, and Yu have developed the theory of Atoms as an ``A side and ``B side'' patching to study birational geometry. The main revolution comes from applying Gromov-Witten invariants to birational geometry problems.
On the other hand, recent developments (in the works of Tschinkel and Kresch) led to the concept of birational maps and rationality equivalence for stacks. Moreover, a cohomology theory based on Gromov-Witten invariants properly captures the cohomological aspects of Deligne-Mumford stacks. In the orbifold case, this is known as Chen-Ruan cohomology. In this talk, we briefly outline the reasoning of atoms and explain how this can be extended to stacks via some toy models. This theory, among other questions, aims to relate birational geometry invariants with differential topology ones via understanding stacks as moduli spaces for smooth structures on some homotopy spheres.
These considerations are part of an ongoing collaboration with L.Grama, L. Katzarkov, and M. Kontsevich.
On the other hand, recent developments (in the works of Tschinkel and Kresch) led to the concept of birational maps and rationality equivalence for stacks. Moreover, a cohomology theory based on Gromov-Witten invariants properly captures the cohomological aspects of Deligne-Mumford stacks. In the orbifold case, this is known as Chen-Ruan cohomology. In this talk, we briefly outline the reasoning of atoms and explain how this can be extended to stacks via some toy models. This theory, among other questions, aims to relate birational geometry invariants with differential topology ones via understanding stacks as moduli spaces for smooth structures on some homotopy spheres.
These considerations are part of an ongoing collaboration with L.Grama, L. Katzarkov, and M. Kontsevich.