Time: 09:30-10:30, Thursday, November 25th, 2021
ZOOM ID: 851 1890 5999
Passcode：761930
Host: Dr. Guodu Chen
Speaker: Dr. Qianyu Chen, Stony Brook University
Title: Limits of Hodge structures via D-modules
Biography:
Qianyu Chen is a PhD student at Stony Brook University. He is interested in Algebraic geometry. Specifically, he studies Hodge theory and D-modules.
Abstract:
It is well-known that each cohomology group of compact K\"ahler manifold carries a Hodge structure. If we consider a degeneration of compact K\"ahler manifolds over a disk then it is natural to ask how the Hodge structures of smooth fibers degenerate. When the degeneration only allows a reduced singular fiber with simple normal crossings (i.e. semistable), Steenbrink constructed the limit of Hodge structure algebraically. A consequence of the existence of the limit of Hodge structure is the local invariant cycle theorem: the cohomology classes invariant under monodromy action come from the cohomology classes of the total space. In this talk, Dr. Chen will try to explain a method using D-modules to construct the limit of Hodge structure even when the degeneration is not semistable.
