CMSA Algebraic Geometry in String Theory: Singularities of the quantum connection on a Fano variety

SEMINARS, CMSA EVENTS

October 14, 2022 9:30 am - 10:30 am

CMSA, 20 Garden St, G10

Address: 1 Oxford Street, Cambridge, MA 02138 USA

Speaker:

Daniel Pomerleano - UMass Boston

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).

This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/algebraic-geometry-in-string-theory/