Beijing Institute of Mathematical Sciences and Applications

Pengfei Huang , Tao Su , Hao Sun

Junliang Shen

Wednesday, April 17, 2024 10:00 AM - 11:00 AM

A3-2-303

Zoom 242 742 6089 (BIMSA)

Around 2008, de Cataldo, Hausel, and Migliorini proposed the P=W conjecture, which predicts a connection between the topology of the Hitchin system and the Hodge theory of the character variety under the non-abelian Hodge correspondence. Since then, much effort has been devoted to understanding this myterious phenomenon, leading to the discovery of new geometric structures on both the Higgs side and the character variety side. In this talk, I will first review the P=W conjecture, which has been proven as a theorem since 2022 by Maulik-Shen and Hausel-Mellit-Minets-Schiffmann. Then I will discuss a recent attempt, in joint work with Davesh Maulik and Qizheng Yin, to understand this conjecture using Fourier transform. This approach establishes links between derived equivalences and the decomposition theorem, shedding further light on the algebraic cycles/motives associated with the Hitchin system.