Related papers: The Jacquet Langlands correspondence via twisted d…

We establish a McKay correspondence for finite and linearly reductive subgroup schemes of $\mathrm{SL}_2$ in positive characteristic. As an application, we obtain a McKay correspondence for all rational double point singularities in…

We introduce the first completely unsupervised correspondence learning approach for deformable 3D shapes. Key to our model is the understanding that natural deformations (such as changes in pose) approximately preserve the metric structure…

Although the Robinson-Schensted-Knuth correspondence is a classical subject, its study is still active because of new development in last two decades. In this field, fundamental results are sometimes proved by using machineries which may be…

Let $F$ be a non-Archimedean local field and $G$ be the general linear group $\mathrm{GL}_n$ over $F$. Bushnell and Henniart described the essentially tame local Langlands correspondence of $G(F)$ using rectifiers, which are certain…

We write down character formulas for representations of $G_2$ considered in Aubert-Xu, and show that stability for $L$-packets uniquely pins down the Local Langlands Correspondence constructed in Aubert-Xu, thus proving unique…

Motivated by applications to the Langlands program, Aubert-Moussaoui-Solleveld extended Lusztig's generalized Springer correspondence to disconnected reductive groups. We use stacks to give a more geometric account of their theory, in…

In this paper we propose a fully automatic method for shape correspondence that is widely applicable, and especially effective for non isometric shapes and shapes of different topology. We observe that fully-automatic shape correspondence…

We formulate the normalized period conjecture proposed by Ben-Zvi, Sakellaridis and Venkatesh in the framework of the categorical local Langlands correspondence and study its relation to distinction problems. Motivated by the work of Feng…

We prove the classical mirror symmetry conjecture for the mirror pairs constructed by Berglund, H\"ubsch, and Krawitz. Our main tool is a cohomological LG/CY correspondence which provides a degree-preserving isomorphism between the…

The Jacobson-Bourbaki Theorem for division rings was formulated in terms of corings by Sweedler in 1975. Finiteness conditions hypotheses are not required in this new approach. In this paper we extend Sweedler's result to simple artinian…

These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…

Based on \cite{DH94}, we introduce a bijective correspondence between first order differential calculi and the graph structure of the symmetric lattice that allows one to encode completely the interconnection structure of the graph in the…

We describe the construction and properties of a singular theta lift for the orthogonal group $\SO(2,1)$. We obtain locally harmonic Maass forms in the sense of Bringmann-Kane-Kohnen with singular sets along geodesics in the upper half…

Given a prime $p$, a finite extension $L/\mathbb{Q}_{p}$, a connected $p$-adic reductive group $G/L$, and a smooth irreducible representation $\pi$ of $G(L)$, Fargues-Scholze recently attached a semisimple Weil parameter to such $\pi$,…

The Lewis-Zagier correspondence, which attaches period functions to Maa\ss\ wave forms, is extended to wave forms of higher order, which are higher invariants of the Fuchsian group in question. The key ingredient is an identification of…

In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolongations. We discuss the relation between Lagrangian and…

This paper was first written in 1990, but was never published. In it, the author presents a novel approach to the study of constant curvature spacetimes in 2+1 dimensions. A parameterization of flat 2+1-dimensional domains of dependence is…

Recently, Honda, Kazez and Matic described an adapted partial open book of a compact contact 3-manifold with convex boundary by generalizing the work of Giroux in the closed case. They also implicitly established a one-to-one correspondence…

Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $SL_n (F)$. It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for…

We formulate a conjecture on local geometric Langlands for supercuspidal representations using Yu's data and Feigin-Frenkel isomorphism. We refine our conjecture for a large family of regular supercuspidal representations defined by…