Related papers: Arithmetic Wavefront Sets and Generic $L$-packets

Let $p$ be a prime number, $F $ a non-archimedean local field with residue characteristic $p$, and $R$ an algebraically closed field of characteristic different from $ p$. We thoroughly investigate the irreducible smooth $R$-representations…

Let $\Pi$ be a cohomological cuspidal automorphic representation of ${\rm GL}_{2n}(\mathbb A)$ over a totally real number field $F$. Suppose that $\Pi$ has a Shalika model. We define a rational structure on the Shalika model of $\Pi_f$.…

Let $G$ be a locally elliptic group, $(\Phi,\Psi)$ a complementary pair of Young functions, and $\omega: G \rightarrow [1,\infty)$ a weight function on $G$ such that the weighted Orlicz space $L^\Phi(G,\omega)$ is a Banach $*$-algebra when…

Let $F$ be a non-Archimedean local field of characteristic $0$, let $G$ be the group of $F$-rational points of a connected reductive group defined over $F$ and let $G'$ be the group of $F$-rational points of its quasi-split inner form.…

We introduce Fermi Sets, a universal and physically interpretable neural architecture for fermionic many-body wavefunctions. Building on a ``parity-graded'' representation [1], we prove that any continuous fermionic wavefunction on a…

Let $F$ be a nonarchimedean local field with odd residual characteristic and let $G$ be the $F$-points of a connected reductive group defined over $F$. Let $\theta$ be an $F$-involution of $G$. Let $H$ be the subgroup of $\theta$-fixed…

This is a report on the progress made on a conjecture of Jiang on the upper bound nilpotent orbits in the wave front sets of representations in local Arthur packets of classical groups, which is a natural generalization of the Shahidi…

Let $G$ be a graph and $f: G\rightarrow G$ be a continuous map. We establish a structure theorem which describes the structures of the set $R(f)-\overline{P(f)}$, where $R(f)$ and $P(f)$ are the recurrent point set and the periodic point…

Let $\pi$ be a cuspidal automorphic representation of $\operatorname{GL}_2$ over a totally real number field $F$. Let $K$ be a totally imaginary quadratic extension of $F$. We estimate central values of the $\operatorname{GL}_2 \times…

We prove a conjecture of the first-named author ([J14]) on the upper bound Fourier coefficients of automorphic forms in Arthur packets of all classical groups over any number field. This conjecture generalizes the global version of the…

Let $X$ be a complex manifold, $\pi: E \rightarrow X$ a locally trivial holomorphic fibration with fiber $F$, and $\mathfrak{g}$ a Lie algebra with an invariant symmetric form. We associate to this data a holomorphic prefactorization…

Let $G$ be the group of $F$-points of a split connected reductive $F$-group over a non-Archimedean local field $F$ of characteristic 0. Let $\pi$ be an irreducible smooth self-dual representation of $G$. The space $W$ of $\pi$ carries a…

We investigate the wavelet spaces $\mathcal{W}_{g}(\mathcal{H}_{\pi})\subset L^{2}(G)$ arising from square integrable representations $\pi:G \to \mathcal{U}(\mathcal{H}_{\pi})$ of a locally compact group $G$. We show that the wavelet spaces…

Let $F$ be a local field and $E/F$ be a separable extension of degree $n$. Regard $T=\text{Res}_{E/F} \mathbb{G}_m$ as an elliptic maximal torus of $G=\mathrm{GL}_n$. We can construct an admissible embedding of L-groups…

We study singularity properties of word maps on semisimple algebraic groups and Lie algebras, generalizing the work of Aizenbud-Avni in the case of the commutator map. Given a word $w$ in a free Lie algebra $\mathcal{L}_{r}$, it induces a…

Let $G$ be a connected, simply connected nilpotent group and $\pi$ be a square-integrable irreducible unitary representation modulo its center $Z(G)$ on $L^2(\mathbf{R}^d)$. We prove that under reasonably weak conditions on $G$ and $\pi$…

The study of random Fourier series, linear combinations of trigonometric functions whose coefficients are independent (in our case Gaussian) random variables with polynomially bounded means and standard deviations, dates back to Norbert…

Given a locally compact quantum group $\mathbb G$, we study the structure of completely bounded homomorphisms $\pi:L^1(\mathbb G)\rightarrow\mathcal B(H)$, and the question of when they are similar to $\ast$-homomorphisms. By analogy with…

Let X be an affine spherical variety, possibly singular, and $L^+X$ its arc space. The intersection complex of $L^+X$, or rather of its finite-dimensional formal models, is conjectured to be related to special values of local unramified…

Full-waveform inversion (FWI) is a powerful seismic imaging technique used to estimate high-resolution physical properties of subsurface structures by minimizing the misfit between observed and modeled seismic data. FWI is inherently a…