Connecting Geometric Galois Actions with Engineering and Group Theory
Speaker: Nigel Boston (University of Wisconsin-Madison)
Date: Thu 31st May 2012
Location: Mathematical Sciences Seminar Room (Ag 1.01)
The absolute Galois group of Q, G_Q, is the automorphism group of the field K of algebraic numbers. It occupies a fundamental role in number theory, yet is still largely mysterious. One approach is to compare the topological properties of a projective variety X over K with those of X^g (g in G_Q). In dimension 1, X and X^g are homeomorphic and further study leads into Grothendieck's dessins d'enfants.
In 1964 Serre constructed examples of X and X^g which have non-isomorphic fundamental groups and are therefore non-homeomorphic. A systematic approach to do this is provided by Beauville surfaces. The first half of this talk will review this state of affairs. The second half will discuss the speaker's work connecting dessins with the Belgian Chocolate Problem in control theory and discovering new examples of Beauville surfaces related to p-groups.
(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)