MS Seminar (Mathematics - String Theory)

Speaker: John Alexander Cruz Morales (Universidad Nacional de Colombia (National U of Colombia))
Title: Revisiting Dubrovin conjecture: GLSM models and integrality of Stokes matrices
Date (JST): Tue, Jul 30, 2024, 13:30 - 15:00
Place: Seminar Room A
Abstract: In 1998 Dubrovin conjectured that for a Fano manifold X the big quantum cohomology QH(X) is (generically) semisimple iff there exists a full exceptional collection in the bounded derived category of X. In addition, the Stokes matrices for the (extended) quantum connection should equal the Gram matrices of the collection.
In this talk we will revisit this conjecture with the glasses of Gauged Linear Sigma Models and working with the CP^n-model with twisted masses we will show how to get integral Stokes matrices for certain semisimple Frobenius manifolds (beyond the quantum cohomology cases) and will discuss how this integrality coincides with the one obtained by Mochizuki in his study of meromorphic flat bundles associated to Toda-like harmonic bundles. This is based on work in progress with J. Chen and M. Romo.