MATH Seminar

Title: Probabilistic Galois theory
Colloquium: Number Theory
Speaker: David Zywina of University of Pennsylvania
Contact: Susan Guppy, sguppy@emory.edu
Date: 2011-02-17 at 4:00PM
Venue: MSC W201
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Abstract: A special case of Hilbert's irreducibility theorem says that a ``random" degree $n$ polynomial with integer coefficients will have the largest possible Galois group (i.e., the symmetric group on $n$ letters). Historically, the notion of ``random" used is that of natural density; the goal of this talk is to discuss alternate approaches that use legitimate probabilistic methods. This will lead us to consider random walks on certain graphs and their connection with the arithmetic of linear algebraic groups.