Westlake Online Math Forum第十九期 | Qizheng Yin: From the Beauville decomposition to the P = W conjecture

2024-04-12 11:08:01



ZOOM ID:967 9950 2530

PASSCODE: 323015

主持人: 理论科学研究院 魏传豪

主讲人: 北京大学 訚琪峥

主讲人介绍: 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.

讲座主题:From the Beauville decomposition to the P = W conjecture


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.