Algebraic Geometry Seminar: "Hodge theory and o-minimality"

Abstract: The cohomology groups of complex algebraic varieties come equipped with a powerful invariant called a Hodge structure.  Going back to foundational work of Griffiths, Hodge theory has found many important applications to algebraic and arithmetic geometry, but its intrinsically analytic nature often leads to complications.  Recent joint work with Y. Brunebarbe, B. Klingler, and J. Tsimerman has shown that in fact many Hodge-theoretic constructions can be carried out in an intermediate geometric category, and o-minimality provides the crucial tameness hypothesis to make this precise.  In this talk I will describe how this perspective can be used to easily recover an important theorem of Cattani--Deligne--Kaplan on the algebraicity of Hodge loci and to prove a conjecture of Griffiths on the quasiprojectivity of the images of period maps.

Host: Matt Kerr