Time：13:00-15:00, Monday, July 24 2023
ZOOM ID: 935 3405 3261
PASSCODE: 042321
Host: Chuanhao Wei, ITS
Speaker：Christian Schnell，Stony Brook University
Biography: Christian Schnell received his Ph.D. from Ohio State University in 2008, with Herb Clemens; after that, he was a postdoc at the University of Illinois at Chicago and at Kavli IPMU near Tokyo. Since 2012, he has been working at Stony Brook University. He studies the geometry and topology of complex algebraic varieties. His research focuses on Hodge theory, and on applications of mixed Hodge modules in algebraic geometry.
Title：Hodge theory and Lagrangian fibrations
Abstract:
A holomorphic symplectic manifold is a (maybe non-compact) Kaehler manifold $X$ of dimension $2n$ with a holomorphic 2-form $\sigma$ that is closed and nondegenerate. A Lagrangian fibration is a proper surjective holomorphic map from $X$ to an $n$-dimensional manifold such that $\sigma$ restricts trivially to every smooth fiber. (The smooth fibers are then automatically $n$-dimensional abelian varieties.) The most famous example is the Hitchin fibration on the moduli space of Higgs bundles, which is used forexample in Ngo's proof of the fundamental lemma and in the P=W conjecture of Mark de Cataldo, Tamas Hausel, and Luca Migliorini. There are several beautiful conjectures about the Hodge theory of such Lagrangian fibrations, discovered by Junliang Shen, Qizheng Yin, and Davesh Maulik.I will give an introduction to these conjectures and their proofs.
