Dubrovin's conjecture for IG(2,6)

Abstract:

For a smooth projective algebraic variety, according to a conjecture of Dubrovin, the semisimplicity of quantum cohomology is related to the existence of full exceptional collections in the derived category of coherent sheaves. I will start by giving a general introduction to quantum cohomology and, eventually, talk about a recent joint work with S. Galkin and A. Mellit on Dubrovin’s conjecture for the symplectic isotropic Grassmannian IG(2,6). This appears to be the simplest case where one needs to work with the big quantum cohomology to formulate the conjecture.