The site at UBC collecting the work of Robert Langlands is now no longer being maintained. There’s a new site now at the IAS. It includes some interesting recent short articles of various kinds that I hadn’t seen before, including a short autobiographical memoir, an expository piece written for Pour La Science, and another piece which includes extensive speculative remarks about his current thinking on the topic of the “Langlands Program”.
The expository piece includes remarks about the remarkable centrality of representation theory both in number theory and quantum theory:
La leçon que nous voulons tirer de ce dicton, “il se trouve derrière tout nombre quantique une representation d’un groupe”, c’est que tomber en mathématiques ou en physique sur les représentations d’un groupe, c’est souvent tomber sur une veine d’or à laquelle il faut tenir corps et âme.
(“The lesson we would like to draw from this motto [due to Weyl] ‘behind every quantum number is a group representation’, is that when one comes upon group representations in mathematics or physics, one has often come upon a vein of gold, which one must pursue body and soul.”)
On the geometric Langlands front, earlier this month the Clay Mathematics Institute organized a series of talks at RIMS in Kyoto by Bezrukavnikov, Gaitsgory and Nakajima about various aspects of the subject. Unfortunately notes from the lectures don’t seem to be available anywhere that I have looked.
Last week the KITP in Santa Barbara hosted a mini-conference on Dualities in Physics and Mathematics, with some of the talks devoted to topics relating geometric Langlands and quantum field theory.