Wednesday September 04, 2019 4:00 PM  5:30 PM Math Tower P131
 Mirko Mauri, Imperial College London
The essential skeletons of pairs and the geometric P=W conjectureThe geometric P=W conjecture is a conjectural description of the asymptotic behavior of a celebrated correspondence in nonabelian Hodge theory. In particular, it is expected that the dual boundary complex of the compactification of character varieties is a sphere. In a joint work with Enrica Mazzon and Matthew Stevenson, we manage to compute the first nontrivial examples of dual complexes in the compact case. This requires to develop a new theory of essential skeletons over a triviallyvalued field. As a byproduct, inspired by these constructions, we show that certain character varieties appear in degenerations of compact hyperKähler manifolds. In this talk we will explain how these new nonarchimedean techniques can shed new light into classical algebraic geometry problems.

Wednesday September 11, 2019 4:00 PM  5:30 PM Math Tower P131
 Thorsten Herrig, Humboldt Universität zu Berlin
Fixed points and entropy of endomorphisms on complex toriWe investigate the fixedpoint numbers and entropies of endomorphisms on complex tori. Motivated by an asymptotic perspective, we study how the number of fixed points behaves when the endomorphism is iterated.
In this talk I show that the fixedpoints function can have only three kinds of behaviour, and I characterize them in terms of the analytic eigenvalues. An interesting followup question is to determine criteria to decide of which type an endomorphism is. I will provide such criteria for simple abelian varieties in terms of the possible types of endomorphism algebras. The gained insight into the occurring eigenvalues can be applied to questions about the entropy of an endomorphism. I will give criteria for an endomorphism to be of zero or positive entropy and will provide examples of automorphisms on simple abelian varieties of dimension four whose entropy is the logarithm of a Salem number.

Wednesday September 18, 2019 4:00 PM  5:30 PM Math Tower P131
 Margaret Bilu, Courant Institute of Mathematical Sciences
TBATBA

Wednesday September 25, 2019 4:00 PM  5:30 PM Math Tower P131
 Enrica Mazzon, Imperial College London
TBATBA

Wednesday October 02, 2019 4:00 PM  5:30 PM Math Tower P131
 TBA, TBA
TBATBA

Wednesday October 09, 2019 4:00 PM  5:30 PM Math Tower P131
 TBA, TBA
TBATBA

Wednesday October 16, 2019 4:00 PM  5:30 PM Math Tower P131
 TBA, TBA
TBATBA

Wednesday October 23, 2019 4:00 PM  5:30 PM Math Tower P131
 TBA, TBA
TBATBA

Wednesday October 30, 2019 4:00 PM  5:30 PM Math Tower P131
 Eyal Markman, University of Massachusetts, Amherst
TBATBA

Wednesday November 06, 2019 4:00 PM  5:30 PM Math Tower P131
 Chenyang Xu,
TBATBA

Wednesday November 13, 2019 4:00 PM  5:30 PM Math Tower P131
 TBA, TBA
TBATBA

Wednesday November 20, 2019 4:00 PM  5:30 PM Math Tower P131
 TBA, TBA
TBATBA

Wednesday December 04, 2019 4:00 PM  5:30 PM Math Tower P131
 TBA, TBA
TBATBA

