David Meretzky : New Constants in Differential Galois Theory

Posted by Ronnie Nagloo , part of the Logic Seminar.

At

April 5, 2022, 4 p.m.

In

427 SEO

Abstract

Picard-Vessiot theory is well behaved over differential fields with algebraically closed fields of constants. Under this assumption PV extensions for an ordinary linear homogeneous differential equation exist and are unique inside of a fixed differential closure. For general fields of constants, one no longer has uniqueness and there is an ``indirect" Galois correspondence. We describe the more limited Galois correspondence for differential extensions which are generated by a fundamental system and possibly allow some new constants. We discuss the general model theoretic context.

Please note that we are not in the usual room