The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and ’t Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlan...

We propose a geometric interpretation of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program. We show that the geometric Langlands conjecture for an irreducible unramified local system E of rank n on a curve implies the existence of automorphic sheaves corresponding to the universal deformation of E. Then we calculate the ‘scalar product’ of two aut...

We show that local-global compatibility away from p holds at points on the (p-adic) eigenvariety of a definite unitary group which are étale over weight space. The novelty is we allow non-classical points. More precisely we interpolate the local Langlands correspondence across the eigenvariety by considering the stalks of its defining coherent sheaf. We employ techniques of Scholze from his rec...

It is a deep fact that the homotopy classification of topological manifolds is convariantly functorial. In other words, a map M → N of topological manifolds naturally induces a map S(M) → S(N) of their structure sets. We extend the fact to the isovariant structure set SG(M, rel Ms) of G-equivariant topological manifolds isovariantly homotopy equivalent to M and restricts to homormorphism on the...

This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The properties of the Bessel models under induction are studied, and an analogue of Rodier’s theorem concerning the induction of Whittaker models is proved for ...

Representations of affine and graded Hecke algebras associated to Weyl groups play an important role in the Langlands correspondence for the admissible representations of a reductive p-adic group. We work in the general setting of a graded Hecke algebra associated to any real reflection group with arbitrary parameters. In this setting we provide a classification of all irreducible representatio...

The concept of iteration theory of Bloom and Ésik summarizes all equational properties that iteration has in usual applications, e.g., in Domain Theory where to every system of recursive equations the least solution is assigned. However, this assignment in Domain Theory is also functorial. Yet, functoriality is not included in the definition of iteration theory. Pitty: functorial iteration theo...