John Baldwin : The unreasonable effectiveness of model theory in analysis

Posted by John Baldwin , part of the Logic Seminar.

At

Nov. 21, 2017, 4 p.m.

In

SEO 427

Abstract

We attempt to delineate the characteristics of model theory that account for its impact across mathematics. The {\em formalization} of {\em 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. We distinguish two ways in which model theory provides tools to `tame' analysis via first order logic: {\em Axiomatic Analysis} and {\em Definable Analysis}. In this talk we focus on Axiomatic Analysis and specifically in the use of the model theory of differentially closed fields to address century old problems around the transcendence of solutions of to Painlev{\'e} equations. Thus we give some context for recent papers of Pillay, Nagloo, and Freitag.