Seminar| Institute of Mathematical Sciences
Time：Friday, Apirl 16th, 2021, 09:30-10:30
Speaker: Ruijie Yang, Stony Brook University
Abstract: In this talk, I would like to present a new and geometric proof of Sabbah's Decomposition Theorem, which asserts that any semisimple local system remains semisimple after taking the direct image under proper algebraic maps. Sabbah's proof is D-module-theoretic in nature and relies on his theory of polarizable twistor D-modules, which generalizes Saito's theory of polarizable Hodge modules. Instead, we combine the topological approach developed by De Cataldo-Migliorini and Simpson's theory of mixed twistor structures to give the new proof. Along the way, we obtain new results about the cohomology of semisimple local systems. Joint work with Chuanhao Wei.
Conference zoom number: 946 9749 6371