Prof. Andy Schultz - Galois embedding problems, part 1
Channel: usnamathweb
Date: 2014-04-10

This is part 1 of the talk.

Title: A new method for finding solutions to certain Galois embedding problems

Speaker: Prof. Andy Schultz, Wellesley College

Abstract:
One of the major open problems in Galois theory is the inverse Galois problem: for a given group G and field F, how does one detect if F has an extension L whose Galois group is G? One can approach this problem inductively when G has a nontrivial quotient Q by using the short exact sequence from Galois theory; this leaves us with a relativized version of the inverse Galois problem which is called a Galois embedding problem. Typically one analyzes embedding problems by performing calculations in second cohomology. For a certain class of groups, we describe a new technique that relies instead on basic linear algebra. This allows us to give precise enumeration results for a wide class of embedding problems and puts fairly severe restrictions on the structure of absolute Galois groups.

See 

http://arxiv.org/abs/1109.4071

http://arxiv.org/abs/1109.4070

http://arxiv.org/pdf/math.NT/0409532