Fundamentals on (G-equivariant) atoms

Abstract:

In this talk, we introduce the concept of atoms recently introduced by Katzarkov-Kontsevich-Pantev-Yu. Built from Gromov-Witten theory, they have been proven to be useful in understanding questions in birational geometry by examining the behavior of quantum cohomology under blowup (this is a theorem of H. Iritani, following a conjecture of M. Kontsevich). After becoming familiar with some examples, this talk explains how the theory can be extended to the G-equivariant setting, where G is generally a finite subgroup of automorphisms of smooth projective varieties over ( mathbb ). Our results are obtained in collaboration with L. Grama, L. Katzarkov, and M. Kontsevich.