UCSB Distinguished Lectures in the Mathematical Sciences
Ron Donagi, May 1213, 2008
Monday, May 12, 2008, 3:30 p.m. South Hall 6635 (Refreshments at 3:00 p.m.) 
Ron Donagi University of Pennsylvania Arithmetic and Geometry, Abelian and Non Abelian Abstract: We will describe the Langlands program in general as a conjectural non abelian analogue of well known "abelian" results: class field theory on the arithmetic side, and the AbelJacobi theory of Riemann surfaces and their Jacobians on the geometric side. One powerful approach to the geometric Langlands conjectures involves abelianization via Hitchin's integrable system and its spectral curves.

Tuesday, May 13, 2008, 3:30 p.m. South Hall Room 6635 
Ron Donagi University of Pennsylvania Algebra and Analysis, Classical and Quantum Abstract: Recent input from physics suggests that the geometric Langlands conjecture, as formulated by Deligne, Laumon, Beilinson and Drinfeld, can be viewed as a statement in quantum field theory. This has a classical limit which has now been proved, at least generically. The relationship between the classical and quantum versions is deep and mysterious. The quantum version can of course be studied as a deformation of the classical one. But there is tantalizing evidence  from quantum field theory as well as non abelian Hodge theory  that the full quantum version can also be understood as a twistor rotation of the classical version.
