Time：15:00-17:00, Wednesday, April 17 2024
Venue: ZOOM
ZOOM ID: 967 9950 2530
PASSCODE: 323015
Host: Chuanhao Wei, Institute for Theoretical Sciences
Speaker：Qizheng Yin, Peking University
Biography: Qizheng Yin is now an associate professor at Peking University. His research interest is Algebraic Geometry including algebraic cycles, moduli spaces, enumerative geometry, algebraic curves, abelian varieties, K3 surfaces, hyper-Kähler varieties.
Title: From the Beauville decomposition to the P = W conjecture
Abstract:
The cohomology (resp. Chow ring, motive) of an abelian scheme admits a canonical decomposition known as the Beauville decomposition. It provides a multiplicative splitting of the Leray filtration for the abelian scheme. In this talk I will present an extension of the Beauville decomposition for certain abelian fibrations with singular fibers. I will explain how this leads to the multiplicativity of the perverse Leray filtration for such fibrations, and eventually to a new proof of the P = W conjecture. If time permits, I will also discuss the case of Lagrangian fibrations (including the Hitchin fibration), with a focus on the Chow-theoretic (resp. motivic) enhancements of several known cohomological structures. This is joint work with Younghan Bae, Davesh Maulik, and Junliang Shen.
