Representation Theory Seminar

Thu, 10/05/2012 15:00	Alex Paulin (University of Nottingham)	Representation Theory Seminar	L3
	The p-adic Geometric Langlands Correspondence
	The geometric Langlands correspondence relates rank n integrable connections on a complex Riemann surface $X$ to regular holonomic D-modules on $Bun_n(X)$ , the moduli stack of rank n vector bundles on $X$ . If we replace $X$ by a smooth irreducible curve over a finite field of characteristic p then there is a version of the geometric Langlands correspondence involving $l$ -adic perverse sheaves for $l\neq p$ . In this lecture we consider the case $l=p$ , proposing a $p$ -adic version of the geometric Langlands correspondence relating convergent $F$ -isocrystals on $X$ to arithmetic $D$ -modules on $Bun_n(X)$ .

Thu, 10/05/2012 15:00	Alex Paulin (Nottingham)	Representation Theory Seminar	L3
	The p-adic Geometric Langlands Correspondence
	The geometric Langlands correspondence relates rank n integrable connections on a complex Riemann surface $X$ to regular holonomic D-modules on $Bun_n(X)$, the moduli stack of rank n vector bundles on $X$. If we replace $X$ by a smooth irreducible curve over a finite field of characteristic p then there is a version of the geometric Langlands correspondence involving $l$-adic perverse sheaves for $l\neq p$. In this lecture we consider the case $l=p$, proposing a $p$-adic version of the geometric Langlands correspondence relating convergent $F$-isocrystals on $X$ to arithmetic $D$-modules on $Bun_n(X)$.

Thu, 31/05/2012 14:00	Prof Joel Kamnitzer	Representation Theory Seminar	L3
	Affine MV polytopes and preprojective algebras
	Mirkovic-Vilonen polytopes are a combinatorial tool for studyingperfect bases for representations of semisimple Lie algebras. Theywere originally introduced using MV cycles in the affine Grassmannian,but they are also related to the canonical basis. I will explain howMV polytopes can also be used to describe components of Lusztig quivervarieties and how this allows us to generalize the theory of MVpolytopes to the affine case.

Forthcoming Seminars