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.
Speaker Intro
Ben Davison is a Professor of Geometry and Representation Theory at the University of Edinburgh. He started his current role in June 2024 and previously served as a Reader at the university. Davison completed his D.Phil. in Mathematics at the University of Oxford in 2011, winning multiple academic prizes. His research interests include representation theory, algebraic geometry, and noncommutative algebraic geometry. He has held prestigious postdoctoral positions at institutions like EPFL Lausanne and Universität Bonn, and received numerous awards, including the Royal Society University Research Fellowship and the ERC Starting Grant. Davison has delivered invited talks at international conferences and authored influential publications.