Tom A Bridgeland: Geometric structures defined by Donaldson-Thomas invariants

Abstract : In recent work the author has explored the idea that the DT invariants of a three-dimensional Calabi-Yau category can be used to define a geometric structure on the space of stability conditions. The relevant structure was christened a Joyce structure and can be viewed as a kind of non-linear Frobenius structure. There are close links with hyperkahler structures and the work of Gaiotto,...

Changzheng Li：Automorphisms of the quantum cohomology of the Springer resolution and applications

Abstract.In this talk, we will introduce quantum Demazure--Lusztig operators acting by ring automorphisms on the equivariant quantum cohomology of the Springer resolution. Our main application is a presentation of the torus-equivariant quantum cohomology in terms of generators and relations. We will discuss explicit descriptions for the classical types. We also recover Kim's earlier results fo...

Todor Milanov：Reflection vectors and quantum cohomology of blowups

Abstract: Let X be a smooth projective variety with a semi-simple quantum cohomology. The monodromy group of the quantum cohomology is by definition the monodromy group of the so-called second structure connection. There is a very interesting conjecture, more or less equivalent to Dubrovin's conjecture, that gives an explicit description of the monodromy group in terms of the exceptional objec...