Related papers: On the Stable Transfer for $\mathrm{Sym}^{n}$ Lift…

Lifting theorems form an important collection of tools in showing that Galois representations are associated to automorphic forms. (Key examples in dimension n>2 are the lifting theorems of Clozel, Harris and Taylor and of Geraghty.) All…

In this note, we derive explicitly the local relative trace formula for the symmetric space F*\SL(2,F) at the level of Lie algebras, where F is a p-adic field of residue characteristic greater than two and F* is the set of invertible…

We study the renormalization group flow in a class of scalar-tensor theories involving at most two derivatives of the fields. We show in general that minimal coupling is self consistent, in the sense that when the scalar self couplings are…

Let $F$ be a non-Archimedean local field. Let $\mathcal{A}_n(F)$ be the set of equivalence classes of irreducible admissible representations of $\textrm{GL}_n(F)$, and $\mathcal{G}_n(F)$ be the set of equivalence classes of n-dimensional…

In this paper, we prove the local converse theorem for $\textrm{Sp}_{2r}(F)$ over a $p$-adic field $F$. More precisely, given two irreducible supercuspidal representations of $\textrm{Sp}_{2r}(F)$ with the same central character such that…

Let $F$ be a non-Archimedean local field. This paper studies homological properties of irreducible smooth representations restricted from $\mathrm{GL}_{n+1}(F)$ to $\mathrm{GL}_n(F)$. A main result shows that each Bernstein component of an…

In this paper we give the detailed error analysis of two algorithms $W_1$ and $W_2$ for computing the symplectic factorization of a symmetric positive definite and symplectic matrix $A \in \mathbb R^{2n \times 2n}$ in the form $A=LL^T$,…

In recent work, the authors proved a general result on lifting $G$-irreducible odd Galois representations $\mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_{\ell})$, with $F$ a totally real number field and $G$ a reductive group, to…

By use of Lagrangian tracers propagated on 2D simulations of Scrape-Off Layer (SOL) turbulence, we are able to determine the non-local fractional-advection, fractional-diffusion equation (FADE) coefficients for a number of equilibrium…

The composition $\mathcal{F} \circ \mathcal{G}$ of two combinatorial classes $\mathcal{F}$ and $\mathcal{G}$ is a standard combinatorial construction and translates into the composition $F(G(z))$ of their corresponding counting generating…

In this paper, we propose a method based on GMM (the generalized method of moments) to estimate the parameters of stable distributions with $0<\alpha<2$. We don't assume symmetry for stable distributions.

We prove a geometric local constancy theorem for affine Springer fibers in families of close local fields. Consequently, stable orbital integrals are locally constant in these families, and both the base change fundamental lemma and the…

The stable reduction theorem says that a family of curves of genus $g\geq 2$ over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new proof of this…

The celebrated Harish-Chandra's integrability theorem states that the distributional character of an irreducible smooth representation of a p-adic group $G(F)$ is integrable, that is represented by an $L^1_{loc}(G(F))$ function. Here $F$ is…

We study the universal PGL_n$character variety over M_g whose fiber over a point [C] is the space of PGL_n-local systems on the curve C. We use nonabelian Hodge theory and properties of Saito's mixed Hodge modules to show that the…

We determine which faithful irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero. This…

Let $\Gamma$ be either i) the absolute Galois group of a local field $F$, or ii) the topological fundamental group of a closed connected orientable surface of genus $g$. In case i), assume that $\mu_{p^2} \subset F$. We give an elementary…

A theorem of Waldspurger states that the Fourier transform of a stable distribution on the Lie algebra of a simply-connected semisimple group $G$ over a p-adic field, is again stable. We generalize this theorem to representations whose…

A main goal of this paper is to introduce a new description of the stable orbital integral for a regular semisimple element and for the unit element of the Hecke algebra in the case of $\mathfrak{gl}_{n,F}$, $\mathfrak{u}_{n,F}$, and…

Motivated by global applications, we propose a theory of relative endoscopic data and transfer factors for the symmetric pair $(U(2n),U(n)\times U(n))$ over a local field. We then formulate the smooth transfer conjecture and fundamental…