Logic Seminar
John Baldwin
UIC
The unreasonable effectiveness of model theory in Number Theory
Abstract: Emulating Wigner's famous essay we attempt to delineate the
characteristics of model theory that account for its impact across
mathematics. The formalization of specific areas of
mathematics is the basic theme; this allows axiomatizations that
respect the methodologies of each area. Secondly, classification
theory allows the recognition of common methodologies in widely
distinct areas. Thus two large groups of tame areas are
identified: stable (and refinements) and o-minimal. Bourbaki's `great
mother structures': groups, order, topology' are put in perspective
and a 4th mother structure, geometry, takes its place in establishing
dimension as the key to tameness. This organizational survey will be
fleshed out by more specific considerations of interactions with
number theory, identifying specific unifying model theoretic
techniques. Examples include Wilkie-Pila on the Andre-Oort
conjectures and Hrushovski on the function field Mordell-Lang.
Wednesday April 27, 2016 at 10:00 AM in SEO 636