Related papers: The Sakellaridis-Venkatesh Conjecture for $ U(2)\b…

In this paper we characterize irreducible generic representations of $\SO_{2n+1}(k)$ where $k$ is a $p$-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic…

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of $\GL_{1}$ and $\GL_{2}$ automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present…

Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$ and let $G = GL_{2/F}$. Let $\mathbf{q}$ be an indeterminate and let $H^{(1)}(\mathbf{q})$ be the generic pro-p Iwahori-Hecke algebra of the group $G(F)$. Let…

Fix a number field k with its adele ring A. Let G=O(n+3) be an orthogonal group of k-rank 1 and H=O(n+2) a k-anisotropic subgroup. We have previously [arXiv:0908.3521] described how to factor the global period of a spherical Eisenstein…

Let p > 2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call "pseudo-Barsotti-Tate representations", over arbitrary finite extensions of the…

This paper is the second in a series of five that together prove the geometric Langlands conjecture. Our goals are two-fold: (1) Formulate and prove the Fundamental Local Equivalence (FLE) at the critical level; (2) Study the interaction…

In this article, we obtain a complete list of inequivalent irreducible representations of the compact quantum group $U_q(2)$ for non-zero complex deformation parameters $q$, which are not roots of unity. The matrix coefficients of these…

This is the second of a series of four papers in which we prove the following relaxation of the Loebl-Komlos--Sos Conjecture: For every $\alpha>0$ there exists a number $k_0$ such that for every $k>k_0$ every $n$-vertex graph $G$ with at…

In this paper we pursue the refined global Gross-Prasad conjecture for Bessel periods formulated by Yifeng Liu in the case of special Bessel periods for $\mathrm{SO}\left(2n+1\right)\times\mathrm{SO}\left(2\right)$. Recall that a Bessel…

We generalize previous results for the superplane Landau model to exhibit an explicit worldline N = 2 supersymmetry for an arbitrary magnetic field on any two-dimensional manifold. Starting from an off-shell N = 2 superfield formalism, we…

Let F be a local field of characteristic 0. The Breuil-Schneider conjecture for GL_2(F) predicts which locally algebraic representations of this group admit an integral structure. We extend the methods of [K-dS12], which treated smooth…

We compute the second moment of a certain family of Rankin-Selberg $L$-functions L(f x g, 1/2) where f and g are Hecke-Maass cusp forms on GL(n). Our bound is as strong as the Lindel\"of hypothesis on average, and recovers individually the…

{We use the recent proof of Jacquet's conjecture due to Harris and Kudla, and the Burger-Sarnak principle to give a proof about the relationship between the existence of trilinear forms on representations of $GL_2(k_u)$ for a…

The formal degree conjecture and the root number conjecture are verified with respect to supercuspidal representations of $Sp_{2n}(F)$ and $L$-parameters associated with tamely ramified extension $K/F$ of degree $2n$. The supercuspidal…

We decompose into irreducible factors the ${\rm SU}(2)$ Witten-Reshetikhin-Turaev representations of the mapping class group of a genus $2$ surface when the level is $p=4r$ and $p=2r^2$ with $r$ an odd prime and when $p=2r_1r_2$ with $r_1$,…

In this paper, we study the Cauchy problem of the Euler-Nernst-Planck-Possion system. We obtain global well-posedness for the system in dimension $d=2$ for any initial data in $H^{s_1}(\mathbb{R}^2)\times H^{s_2}(\mathbb{R}^2)\times…

We explain how the Harish-Chandra Plancherel Theorem and results in relative Lie algebra cohomology can be used in order to compute in a uniform way the $L^2$-Betti numbers, the Novikov-Shubin invariants, and the $L^2$-torsion of compact…

We establish the existence and uniqueness of twisted exterior and symmetric square $\gamma$-factors in positive characteristic by studying the Siegel Levi case of generalized spinor groups. The corresponding theory in characteristic zero is…

Helmholtz decomposition theorem for vector fields is usually presented with too strong restrictions on the fields and only for time independent fields. Blumenthal showed in 1905 that decomposition is possible for any asymptotically weakly…

We study a generalization of the results \in \cite{cfk} to the case of $SU(1|1)$ interpreted as the supercircle $S^{1|2}$. We describe all of its finite dimensional complex irreducible representations, we give a reducibility result for…