Vahagn Aslanyan : Modular Schanuel, Zilber-Pink, and Existential Closedness with Derivatives

Posted by Ronnie Nagloo , part of the Unlikely Intersections Seminar.

At

April 18, 2023, 2 p.m.

In

636 SEO

Abstract

There are three important conjectures at the boundary between model theory, arithmetic geometry, and complex geometry -- Schanuel, Zilber-Pink, and Existential Closedness. I will discuss these conjectures for the modular j-function and mostly focus on novel versions incorporating the derivatives of j. I will then explain the relationship between them including a new link which is visible only when we consider the derivatives. At the end I will present the functional/differential variants of these conjectures which are all theorems.