Related papers: Hidden sign in Langlands' correspondence
This work is intended as an introduction to the statement and the construction of the local Langlands correspondence for GL(n) over p-adic fields. The emphasis lies on the statement and the explanation of the correspondence.
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
The theory of intertwining operators plays an important role in the development of the Langlands program. This, in some sense, is a very sophisticated theory, but the basic question of its singularity, in general, is quite unknown.…
This is an expanded set of notes based on two lectures given by the author at the 2022 IHES summer school on the Langlands program, on explicit techniques for the construction of automorphic representations.
This article is an overview of the geometrization conjecture for the local Langlands correspondence formulated by the author.
This is a set of notes on automorphic forms and theta correspondence, based on my lectures at the 2022 Arizona Winter School.
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
There are two versions of endoscopic transfer factors to accommodate the different versions, classical or renormalized, of the local Langlands correspondence. An examination of the structure of these complex-valued factors shows that the…
After observing that some constructions and results in the $p$-adic Langlands programme are somehow independent from $p$, we formulate the hypothesis that this astonishing uniformity could be explained by a 1-adic Langlands correspondence.
In this paper, we survey some mathematical developments that followed from the discovery of simple supercuspidal representations of p-adic groups.
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
This note supplements our paper "Induced nets and Hamiltonicity of claw-free graphs", by giving the detailed proof that were omitted in it.
The (Deuring-Heilbronn-) Linnik phenomenon is extended to L-functions associated with real analytic automorphic forms. The repelling effect of exceptional zeros of Dirichlet L-functions are felt not only by those L-functions themselves but…
Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we show how Sato's specialization and microlocalization functors have a natural enhancement, and discuss some of their…
In this paper, we give a method for characterizing the local Langlands conjectures in the vein of Scholze's alternate proof of the local Langlands conjecture for $\mathrm{GL}_n$. More specifically, we show that if a local Langlands…
This study explores the cryptic Voynich Manuscript, by looking for subtle signs of scribal intent hidden in overlooked features of the "Voynichese" script. The findings indicate that distributions of tokens within paragraphs vary…
This is a report on the global aspects of the Langlands-Shahidi method which in conjunction with converse theorems of Cogdell and Piatetski-Shapiro has recently been instrumental in establishing a significant number of new and surprising…
We survey several recent examples of derived structures emerging in connection with the Langlands correspondence. Cases studies include derived Galois deformation rings, derived Hecke algebras, derived Hitchin stacks, and derived special…
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
This note presents an interesting counterexample to a basic covering problem.