Nonabelian Hodge theory for stacks and BPS cohomology
Organizers
Speaker
Ben Davison
Time
Thursday, May 16, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
If C is a smooth projective complex curve, the nonabelian Hodge correspondence gives a diffeomorphism between the coarse moduli space of degree d rank r semistable Higgs bundles on C, and r-dimensional d-twisted representations of the fundamental group of the underlying Riemann surface of C. If r and d are not coprime, there are strictly semistables with nontrivial stabilizers, and it perhaps makes more sense to study the respective stacks, instead of coarse moduli spaces. It seems to be too much to ask that there is any kind of isomorphism between these stacks, but what we can show is that the Borel-Moore homology of the two stacks are naturally isomorphic. The proof uses the classical nonabelian Hodge correspondence, but also a lot of new cohomological DT theory, and a version of the cohomological integrality conjecture for 2-Calabi-Yau categories. This is joint work with Hennecart and Schlegel Mejia.