CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
Coxeter Groups and Certain Differential Equations Rob Maier
May 1, 2012 Math 350 2-3pm	Abstract Coxeter groups occur as both automorphism groups and monodromy groups of certain Fuchsian differential equations. This includes the Picard-Fuchs equations associated to families of elliptic curves (i.e., associated to elliptic surfaces). Such equations are second-order differential equations that are extensions of the Gauss hypergeometric equation (e.g., they may be of the Heun type). The appearance of Coxeter groups as their automorphism groups will be explained, and it will also be briefly explained how Coxeter groups appear as the monodromy groups of certain generalized hypergeometric equations (those with algebraic solutions), as has been known since work of Frits Beukers.

Coxeter Groups and Certain Differential Equations

Rob Maier

May 1, 2012

Math 350

2-3pm

Abstract

Coxeter groups occur as both automorphism groups and monodromy groups of certain Fuchsian differential equations. This includes the Picard-Fuchs equations associated to families of elliptic curves (i.e., associated to elliptic surfaces). Such equations are second-order differential equations that are extensions of the Gauss hypergeometric equation (e.g., they may be of the Heun type). The appearance of Coxeter groups as their automorphism groups will be explained, and it will also be briefly explained how Coxeter groups appear as the monodromy groups of certain generalized hypergeometric equations (those with algebraic solutions), as has been known since work of Frits Beukers.