Ryan Carpenter : Existentialism and Model Theory, or: All Roads Lead to Zilber's Trichotomy Conjecture

Posted by Ryan Carpenter , part of the Louise Hay Logic Seminar.

At

Sept. 10, 2025, 4:30 p.m.

In

427 SEO

Abstract

Transcendental number theory, tropical geometry, and cohomology of complex abelian varieties—to name a few—are some of the areas from which techniques are borrowed to prove existential closedness results that are active areas of research in model theory today. Such techniques (no doubt, the questions they serve to answer) might suggest a sort of existential question for the model theorist: what am I doing in the middle of all this? In this talk, I will detail the existential closedness results model theorists have cared about over the last thirty years, and then I will place these results in their proper historical context to get around to answering the model theorist's existential question.