Seminars & Colloquia Calendar
Hodge theory and o-minimal geometry
Ben Bakker - U. Georgia
Location: Hill 425
Date & time: Wednesday, 02 May 2018 at 2:00PM - 3:00PM
Abstract: Hodge structures on cohomology groups are fundamental invariants of algebraic varieties; they are parametrized by quotients D/? 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/? 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.