SMS scnews item created by James East at Tue 6 Oct 2009 1035
Type: Seminar
Distribution: World
Expiry: 9 Oct 2009
Calendar1: 9 Oct 2009 1205-1255
CalLoc1: Carslaw 375

Algebra Seminar

An introduction to the Geometric Langlands Conjectures -- Part II

John Rice

Friday October 9, 12:05--12:55pm, Carslaw 375


Every one dimensional local system on a compact Riemann surface is the pull back, under the Abel-Jacobi embedding, of a unique such local system on its Jacobian variety. The latter can be extended in a natural way to the whole Picard variety. I will explain this in detail, and in what way it constitutes an analogue of Artin's Reciprocity Law in the case of curves over finite fields and of algebraic number fields. The global Geometric Langlands conjectures are a certain generalisation to bundles of higher rank. I will explain its general features, and illustrate its connection with finite field and number field analogues from whence the conjecture gets its name.

The Langlands conjectures come in local and global forms, as with class field theory, and enjoy a similar complex relationship. The local Geometric Langlands conjectures posit a parametrisation of the 'representations' of complex loop groups by local systems on the formal punctured disc. In a second talk I will explain the ideas of Frenkel and Gaitsgory about what 'representation' should mean in this context, and the implications which flow from this for representations of Kac-Moody algebras at the critical level.


After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East