Logic Seminar
David Meretzky
University of Notre Dame
New Constants in Differential Galois Theory
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
Tuesday April 5, 2022 at 4:00 PM in 427 SEO