Mathematics Tea

The Weil-Étale fundamental group of a number field

Baptiste Morin
Caltech

Lichtenbaum has conjectured the existence of a Weil-étale cohomology for arithmetic schemes such that the special values of the corresponding zeta functions should be given by Euler char- acteristics. We will explain what we can prove about the underlying fundamental group in the case of a number ring. This leads to a description of the conjectural Weil-étale topos and this gives a new computation for the Weil-étale cohomology of number rings.

Is Dispersion a Stabilizing or Destabilizing Mechanism?`

Edriss S. Titi
University of California, Irvine and Weizmann Institute

In this talk I will present a unified approach for the effect of fast rotation and dispersion as an averaging mechanism for, on the one hand, regularizing and stabilizing certain evolution equations. On the other hand, I will also present some results on which large dispersion is a destabilizing mechanism for the long-time dynamics of certain dissipative evolution equations.

Biautomaticity and CAT(0) Groups

Rena Levitt
Pomona College

A closed, compact n-dimensional Riemannian manifold with strictly negative sectional curvatures has a contractible universal cover with unique geodesics, and a fundamental group whose word problem can be solved in linear time. Both of these properties have been generalized. The geometric properties lead to the theory of CAT(0) and nonpositively curved spaces, while the computational properties inspired the theory of automatic and biautomatic groups. This leads to the following question: are groups acting geometrically on CAT(0) spaces biautomatic? In this talk I will discuss these generalizations, and examples CAT(0) groups that are biautomatic, focusing on groups acting on CAT(0) simplicial 3-complexes.

Mathematics Tea