La formule des traces sur les corps de nombres a été introduite par Selberg, puis développée par Arthur. Parmi les applications importantes de la formule des traces d’Arthur-Selberg, on trouve plusieurs cas du principe de fonctorialité de Langlands et l’expression de la cohomologie des variétés de Shimura en termes automorphes. Cependant, pour beaucoup de ces applications, il est nécessaire de ...

This paper begins the project of adapting the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of admissible representations of real groups, to padic groups, continuing in the direction charted by Vogan in his 1993 paper on the Langlands correspondence. This paper presents three theorems in that direction. The first theorem shows how Lusztig’s work on perverse sheaves aris...

2 Homotopy category of a site with interval 2 2.1 Homotopy theory of simplicial sheaves . . . . . . . . . . . . . . 4 2.1.1 Simplicial sheaves . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 The simplicial model category structure . . . . . . . . 5 2.1.3 Local fibrations and resolution lemmas . . . . . . . . . 8 2.1.4 Homotopy limits and colimits. . . . . . . . . . . . . . . 12 2.1.5 Eilenber...

We describe various path homology theories constructed for a directed hypergraph. introduce the category of hypergraphs and notion homotopy in this category. Also, we investigate functoriality invariance introduced groups. provide examples computation these

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to c...

Thu, Nov 16, 3:30pm Matt Szczesny (Boston Univ.) The Langlands program: from arithmetic to conformal field theory This will be a very elementary attempt to trace the sequence of analogies that lead from the Langlands program for global fields to the geometric formulation given by A. Beilinson and V. Drinfeld. I will attempt to explain the formulation of the latter in the language of conformal f...

Abstract Let $f$ f be a cuspidal Hecke eigenform of level 1. We prove the automorphy symmetric power lifting $\operatorname{Sym}^{n} f$ Sym n for every $n \geq 1$ ≥ 1 . establish same result more general class eigenform...

Arthur's conjectures predict the existence of some very interesting unitary representations occurring in spaces automorphic forms. We prove unitarity ``Langlands element'' (i.e., representation specified by Arthur) all unipotent Arthur packets for split real exceptional groups. The proof uses Eisenstein series, Langlands' constant term formula and square integrability criterion, analytic proper...

One of the fundamental problems of local harmonic analysis is to classify the set Π(G) of equivalence classes of irreducible representations of G(F ). The problem separates naturally into two parts. The first is to establish the local Langlands correspondence. This conjecture of Langlands asserts that Π(G) is a disjoint union of finite subsets Πφ, indexed by (equivalence classes of) Langlands p...