# Algebraic Geometry Seminar

The Algebraic Geometry Seminar features talks on all branches of algebraic geometry, as well as related research fields including, and not limited to: number theory, complex geometry, and differential geometry.
Organizer(s):

Please click on seminar title for complete abstract.

There is no seminar on September 26.

October 17, 2017
4:30pm - 5:30pm
##### The Hodge decomposition for some non-Kahler threefolds with trivial canonical bundle.

We show that the \partial\bar{\partial}-lemma holds for the non-Kahler compact complex manifolds of dimension three with trivial canonical bundle constructed by Clemens as deformations of Calabi-Yau threefolds contracted along smooth rational curves with normal bundle of type (-1, -1), at least on an open dense set in moduli. The  proof uses the mixed Hodge structure on the singular fibers and an analysis of the variation of the Hodge filtration for the smooth fibers.

Location
Fine Hall 322
Speaker: Robert Friedman ,
Columbia University
October 24, 2017
4:30pm - 5:30pm
##### Transcendence of period maps

Period domains D can be described as certain analytic open sets of flag varieties; due to the presence of monodromy, however, the period map of a family of algebraic varieties lands in a quotient D/\Gamma by an arithmetic group.  In the very special case when D/\Gamma is itself algebraic, understanding the interaction between algebraic structures on the source and target of the uniformization D\rightarrow D/\Gamma is a crucial component of the modern approach to the André-Oort conjecture.  We prove a version of the Ax-Schanuel conjecture for general period maps X\rightarrow D/\Gamma which...

Location
Fine Hall 322
Speaker: Ben Bakker,
University of Georgia