Titile: Mini-courses on Galois Theory Speaker: Shuvra Gupta, University of Iowa Time: 15:00-16:00, 16:10-17:10 Date: June 29, 30, July 1, 2, 4, 5, 6 Venue: B1044 Prerequisites: solvable groups, basic ring theory, finite fields and p-adic fields Abstract: My current plan is to quickly revise field extensions, norms and traces, talk about separable and inseparable extensions, fundamental theorem (of Galois Theory), finite fields, cyclotomic extensions, cyclic (Kummer, Artin-Schreier) Extensions, Hilbert Theorem 90, some applications of Galois Theory, Infinite Galois Extensions, Algebraic Closures, Transcendental Extensions and a very brief mention of Differential Galois Theory. In particular, we will also speak briefly about Galois representations and Artin L-functions, and give a vague idea of class field theory.