Algebraic Geometry Seminar

Title: Hodge theory and o-minimal geometry
Speaker: Benjamin Bakker
Speaker Info: Univ. of Georgia
Brief Description:
Special Note:

Hodge structures on cohomology groups are fundamental invariants of algebraic varieties; they are parametrized by quotients $D/\Gamma$ of periods domains by arithmetic groups. Except for a few very special cases, such quotients are never algebraic varieties, and this leads to many difficulties in the general theory. We explain how to partially remedy this situation by equipping $D/\Gamma$ with an o-minimal structure, and show that period maps are "definable" with respect to this structure. As a consequence, we obtain an easy proof of a result of Cattani--Deligne--Kaplan on the algebraicity of Hodge loci, a strong piece of evidence for the Hodge conjecture. The proof of the main theorem relies heavily on work of Schmid, Kashiwara, and Cattani--Kaplan--Schmid on the asymptotics of degenerations of Hodge structures. This is joint work with B. Klingler and J. Tsimerman.
Date: Thursday, April 26, 2018
Time: 4:00pm
Where: Lunt 107
Contact Person: Mihnea Popa
Contact email: mpopa@math.northwestern.edu
Contact Phone:
Copyright © 1997-2024 Department of Mathematics, Northwestern University.