Singularities of the quantum connection on a Fano variety

2022-10-14 09:30 - 10:30
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Algebraic Geometry in String Theory Seminar

Speaker: Daniel Pomerleano, UMass Boston

Title: Singularities of the quantum connection on a Fano variety

Abstract: The small quantum connection on a Fano variety is one of the simplest objects in enumerative geometry. Nevertheless, it is the subject of far-reaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are made for manifolds with semi-simple quantum cohomology or more generally for Fano manifolds whose quantum connection is of unramified exponential type at q=\infty.

I will explain a program, joint with Paul Seidel, to show that this unramified exponential type property holds for all Fano manifolds M carrying a smooth anticanonical divisor D. The basic idea of our argument is to view these structures through the lens of a noncommutative Landau-Ginzburg model intrinsically attached to (M, D).