David Meretzky, University of Notre Dame
"A boundedness condition for differential fields"
A field is bounded if it has finitely many extensions of each finite degree. A theorem of Serre says that if a field is bounded then the Galois cohomology of finite linear algebraic groups over that field is finite and can be understood in terms of finite group cohomology. In this talk, we will introduce a boundedness condition for differential fields. This condition will yield an analogous theorem to Serre's in the differential setting, giving some control over Kolchin's differential Galois cohomology for certain classes of differential algebraic groups related to the Picard-Vessiot theory. We will discuss the relationship between Kolchin's cohomology theory and the Picard-Vessiot theory. This is joint work in progress with Anand Pillay.