Maig 2011- Dia 4 de Maig: Sessió especial Gert Heckman (Nijmejen): Monodromy for the Hypergeometric Function.
Abstract: After reviewing some history of the concept of monodromy (in the work by Riemann, Schwarz and Klein on the Gauss hypergeometric function) we discuss the crucial role played by monodromy for the Clausen-Thomae hypergeometric function (work by Beukers and the lecturer from 1989). The algebraic hypergeometric functions (so the ones with finite monodromy) arise naturally from Coxeter group theory. Finally we focus on one particular example (concerning E_8) and explain its relation with the weak form of the prime number theorem, as proved by Tchebycheff (a recent observation of Rodriguez-Villegas).
Nota: El Gert Heckman farà una segona xerrada el dia 6 de Maig al seminari de Geometria algebraica sobre una temàtica similar. Mireu aquí el programa de la xerrada al seminari de Geometria Algebraica.
Friday May 6:
Monodromy for the Spherical Pendulum.
Abstract: In 1980 Hans Duistermaat proved that the energy-momentum map for the spherical pendulum admits no global action-angle coordinates, as a consequence of the obstruction of nontrivial monodromy. After a review of Duistermaat's paper we explain an alternative (and easy) calculation of the monodromy, and explain that his main result is nothing but the classical Picard-Lefschetz formula.