Title: Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture
Speaker: Junliang Shen - MIT

Data: 06 de outubro
Horário: 13:00h
Local: Transmissão online

Abstract: We describe the cohomological structure of the moduli space of stable SL_n Higgs bundles on a curve following the topological mirror symmetry conjecture of Hausel-Thaddeus. For the approach, we establish a connection between:

(a) the moduli space of twisted Higgs bundles by an effective divisor of degree greater than 2g-2, and 

(b) the moduli space of K_C-Higgs bundles, using vanishing cycle functors.

This allows us to apply Ngo's support theorem, which has a simpler form in the case (a) (by Ngo, Chaudouard-Laumon, de Cataldo), to the case of (b) which concerns hyper-Kähler geometries. In particular, this gives a new proof of the Hausel-Thaddeus conjecture proven previously by Gröchenig-Wyss-Ziegler via p-adic integrations. Based on joint work with Davesh Maulik.

Host: Chenyang Xu
Zoom ID: 991 849 3831
Zoom link: https://us02web.zoom.us/j/9918493831?pwd=UWZkTDJ3WG5GMHJRTVQ4STdWeHF4Zz09
Password: October