John Baldwin : The unreasonable effectiveness of model theory in Number Theory

Posted by John Baldwin , part of the Logic Seminar.

At

April 27, 2016, 10 a.m.

In

SEO 636

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.