Matt Wechter : Galois Theories and Differential Algebra

Posted by Paul Reschke , part of the Graduate Student Colloquium.

At

April 16, 2012, 4:15 p.m.

In

SEO 636

Abstract

The Fundamental Theorem of Galois Theory gives correspondences between intermediate subfields of a Galois (separable, splitting) extension and subgroups of automorphisms. I will talk about Jacobson Galois Theory detailing similar correspondences for purely inseparable field extensions of exponent one. Further, I will describe more recent Galois-type correspondences for purely inseparable fields of higher exponent and my attempts to bridge the two approaches using differential algebra. This talk is intended to be accessible to graduate students of all levels; no technical knowledge of differential algebra is expected.