Applications of o-minimality to Hodge theory VI
Organizer
Speaker
Jiaming Chen
Time
Wednesday, January 24, 2024 3:00 PM - 4:30 PM
Venue
A3-1-301
Online
Zoom 293 812 9202
(BIMSA)
Abstract
The goal of this minicourse is to introduce the recent advances in Hodge theory via o-minimal techniques. We will start by revisiting the basics on o-minimal geometry with a view towards algebraization theorems (Pila-Wilkie counting theorem; o-minimal Chow and GAGA theorems in definable complex analytic geometry). In the realm of Hodge theory, we will explore several applications:
(i) the definability of period maps (which enables us to easily recover a theorem of Cattani-Deligne-Kaplan on the algebraicity of Hodge loci) and the algebraicity of images of period maps (Griffiths conjecture);
(ii) Ax-Schanuel for variations of Hodge structures;
(iii) distribution of Hodge loci.