Mathematical Colloquium 
(Some) Explicit Galois Theory 

By  Andrew Obus 
From  Department of Mathematics Columbia University 
When  February 22, 2010 4:00 pm 
Where  Weber 202 
Abstract  In many circumstances, it is useful and interesting to categorize all Galois extensions of a given field in an explicit way. After reviewing some fields where this problem is easily solved, we will turn our attention to the Laurent series field K = k((t)), where k is an algebraically closed field of characteristic p > 0. Recent work of the speaker and Rachel Pries has explicitly classified all extensions L/K where Gal(L/K) is an extension of a primetop group by a cyclic group. We will discuss these results and their relation to algebraic geometry, in particular, the problem of lifting varieties and automorphisms from characteristic p to characteristic 0. 
Further Information 
Rachel Pries 
There will be Refreshments in Weber 117 at 3.30pm
The Colloquium counts as Seminar Credit for Mathematics Students.