Nov 17 at 17:30 in 507

Title:  Wall-crossing, non-abelian localization, and Fano threefolds.

Abstract: Despite the general progress concerning wall-crossing formulas for Donaldson-Thomas invariants of quasi-smooth stacks (in the works of Joyce, Liu, et al.), several important questions remained unanswered up to a recent time. Quite surprisingly, e.g., some issues of similar flavor were an obstacle to:

A) cross walls for moduli of objects in the derived category;

B) prove Bu’s conjecture on self-orthogonal wall-crossing.

We replace Joyce’s original proof with the one based on the work of Daniel Halpern-Leistner, and remove this obstacle. Time permitting, I will explain applications to the Feyzbakhsh-Thomas programme, and to the PT-rationality for Fano threefolds. This is a joint work with Miguel Moreira.