Geometry, Topology and Dynamics Seminar
Tim Gendron
Universidad Nacional Autonoma de Mexico
Geometric and Arithmetic Irrationality through Substructures of Nonstandard Models
Abstract: We explore the idea that nonstandard models of a standard algebraic
object function like lenses of a microscope with which one may perceive
irrationality invisible to the standard model. We illustrate this philosophy
using the ultraproduct construction, in the context of the following three
examples:
- Algebraic topology of foliated spaces (the fundamental germ).
- Algebraic number theory of the reals (diophantine approximation groups).
- Modular invariants of quantum tori (Kronecker foliations)
Wednesday February 24, 2010 at 3:00 PM in SEO 612