Michael Lange of UIC : Find me a Field

Posted by Hazal Sena Aydogdu , part of the Louise Hay Logic Seminar.

At

Sept. 16, 2026, 11 a.m.

In

427 SEO

Abstract

The Algebraicity Conjecture of Cherlin and Zilber proposes that every simple group of finite Morley rank is abstractly isomorphic to the $K$-points of some algebraic group for some algebraically closed field $K$. The goal of this talk will be to present two early results fundamental to the study of such groups. One, a "linearization lemma" due to Zilber, demonstrates one natural way in which interpretable fields can arise from definable group actions; the other, MacIntyre's Theorem on $\omega$-stable fields, explains why all such fields must be algebraically closed.