Large fields were introduced by F. Pop and proved to be the “right class” of fields over which to study inverse Galois theory and other algebraic objects. Differential Galois Theory classically considered differential fields with algebraically closed fields of constants, but more recently interest in more general constant fields has grown. In this talk, we focus on differential fields whose fields of constants are large and of infinite transcendence degree over the rationals. In particular, we study the inverse problem as well as embedding problems over such fields.
This is joint work with A. Bachmayr, D. Harbater, and F. Pop. The work was supported by the NSF FRG grant DMS-1463733 and by the Simons Foundation (Simons fellowship).