Geometric application of p-adic integration formalism

Time: 9:30 -- 11:00, April 19th, 2023.
Venue: Room 612, A6, Institute of Mathematics, VAST
Abstract: In 2017, through the application of p-adic integration to the Hitchin integrable system, Groechenig, Wyss and Ziegler (GWZ) proved the (non-parabolic version of) topological mirror symmetry (conjectured by Hausel and Thaddeus, in which they predicts a correspondence between the Hodge numbers of the moduli spaces of SL(n)-Higgs bundles and the moduli spaces of PGL(n)-Higgs bundles). Using the same approach, in 2019, they extended their work to a general pair of Langlands dual groups $(G,hat{G})$ and obtained a new proof for Ngo's geometric stabilization theorems. In this talk, I will try to explain the work of GWZ.