|Date: Friday, September 24, 2021
Location: 2866 East Hall (3:00 PM to 4:00 PM)
Title: Hodge theory and numerical invariants of algebraic varieties
Abstract: When a compact complex manifold is given as the vanishing locus of polynomial equations, its singular cohomology groups possess natural direct-sum decompositions called Hodge structures. These Hodge structures strongly influence the topology of the variety; for instance, their mere existence implies that the odd-degree cohomology groups have even rank. I will explain what these structures are and how they lead to nice discrete invariants of algebraic varieties, such as Hodge numbers and Hodge diamonds. I will also discuss connections to the Grothendieck ring of varieties.
Speaker: James Hotchkiss