Taking advantage of the quantale-theoretic description \'etale groupoids we study principal bundles, Hilsum-Skandalis maps, and Morita equivalence in terms modules on inverse quantal frames. The Hilbert module quantale sheaves leads naturally to a formulation bimodules that resemble imprimitivity C*-algebras.

The main goal of the School was to introduce graduate students and young mathematicians to three broad and interrelated areas in the theory of automorphic forms. Much of the volume is comprised of the articles of Arthur, Kottwitz, and Milne. Although these articles are based on lectures given at the school, the authors have chosen to go well beyond what was discussed there, in order to provide ...

We construct an explicit equivalence between the (bi)category of gl(2) webs and foams Bar-Natan Temperley-Lieb diagrams cobordisms. With this we can fix functoriality every link homology theory that factors through category. To achieve this, define web versions arc algebras their quasi-hereditary covers, which provide strictly functorial tangle homologies. Furthermore, isomorphisms these origin...

Introduction. Whittaker models have been crucial in the development of the theory of automorphic forms. Within the Langlands-Shahidi method, Whittaker models give rise to the definition of local coefficients [Sh1,Sh2], which proved critical in establishing the proof of Langlands’s conjecture relating local L–functions to Plancherel measures for generic representations [Sh3]. This, in turn, led ...

Part I. The origins of the Langlands Program 9 1. The Langlands correspondence over number fields 9 1.1. Galois group 9 1.2. Abelian class field theory 10 1.3. Frobenius automorphisms 13 1.4. Rigidifying ACFT 14 1.5. Non-abelian generalization? 15 1.6. Automorphic representations of GL2(AQ) and modular forms 18 1.7. Elliptic curves and Galois representations 22 2. From number fields to function...

The Langlands functoriality conjecture, as reformulated in the “beyond endoscopy” program, predicts comparisons between (stable) trace formulas of different groups G1,G2 for every morphism G1L→LG2 their L-groups. This conjecture can be seen a special case more general which replaces reductive by spherical varieties and formula its generalization, relative formula. goal this article precursor [1...

A variant of the usual supersymmetric nonlinear sigma model is described, governing maps from a Riemann surface Σ to an arbitrary almost complex manifold M . It possesses a fermionic BRST-like symmetry, conserved for arbitrary Σ, and obeying Q = 0. In a suitable version, the quantum ground states are the 1+1 dimensional Floer groups. The correlation functions of the BRST-invariant operators are...

The local Langlands correspondence is a conjectural connection between representations of groups G(k) for connected reductive groups G over a p-adic field k and certain homomorphisms (Langlands parameters) from the Galois (or WeilDeligne group) of k into a complex Lie group Gwhich is dual, in a certain sense, to G and which encodes the splitting structure of G over k. More introductory remarks ...