Related papers: Murmurations, Periods, and Local Factors

The meaning of local observables is poorly understood in gauge theories, not to speak of quantum gravity. As a step towards a better understanding we study asymptotic (infrared) transformation in local quantum physics. Our observables are…

A Boolean function $f:\{0,1\}^n \to \{0,1\}$ is said to be noise sensitive if inserting a small random error in its argument makes the value of the function almost unpredictable. Benjamini, Kalai and Schramm showed that if the sum of…

We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure attached to Weil-restricted groups, as defined by B. Levin. Our result covers the (modified)…

We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that $$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, \|f\|_{L^1(uv)},$$…

Let $E/\mathbf{Q}$ be a totally real quadratic field. Using unramified harmonic analysis in Hecke modules, we study the $\ell$-adic integral behavior of the (unramified part of the) Asai period attached to a Hilbert modular form for $E$,…

We explore connections between three structures associated with the cohomology of the moduli of 1-dimensional stable sheaves on $\mathbb{P}^2$: perverse filtrations, tautological classes, and refined BPS invariants for local $\mathbb{P}^2$.…

In this paper, we study the following class of weighted Choquard equations \begin{align*} -\Delta u =\lambda u + \Bigg(\displaystyle\int\limits_\Omega \frac{Q(|y|)F(u(y))}{|x-y|^\mu}dy\Bigg) Q(|x|)f(u) ~~\textrm{in}~~ \Omega~~ \text{and}~~…

Let $G$ be the interior domain of a piecewise analytic Jordan curve without cusps. Let $\{p_n\}_{n=0}^\infty$ be the sequence of polynomials that are orthonormal over $G$ with respect to the area measure, with each $p_n$ having leading…

We use weighted polynomial approximation to prove the existence of a compact set K with non-empty interior and a function f is dense in the space A(K) of all continuous functions on K that are holomorphic in the interior of K, endowed with…

Let $K\in L^1(\mathbb R)$ and let $f\in L^\infty(\mathbb R)$ be two functions on $\mathbb R$. The convolution $$(K\ast f)(x)=\int_{\mathbb R}K(x-y)f(y)dy$$ can be considered as an average of $f$ with weight defined by $K$. Wiener's…

We consider smooth area-preserving flows (also known as locally Hamiltonian flows) on surfaces of genus $g\geq 1$ and study ergodic integrals of smooth observables along the flow trajectories. We show that these integrals display a…

In the present note we introduce tame functionals on Banach algebras. A functional $f \in A^*$ on a Banach algebra $A$ is tame if the naturally defined linear operator $A \to A^*, a \mapsto f \cdot a$ factors through Rosenthal Banach spaces…

We show that any Littlewood--Paley square function $S$ satisfying a minimal local testing condition is dominated by a sparse form, \begin{equation*} \langle (Sf)^2,g \rangle\le C \sum_{I \in \mathscr{S}} \langle \lvert f\rvert\rangle_I^2…

Let $K$ be a number field with a finite set $S$ of primes. We study the cohomology of $\mathbb{F}_p[G_{K,S}]$-modules $A$, in particular the Shafarevich groups $\Sha^i_S(K,A)$ for $i=1,2$ for tame sets $S$, i.e., for sets $S$ that contain…

We consider pro-isomorphic zeta functions of the groups $\Gamma(\mathcal{O}_K)$, where $\Gamma$ is a unipotent group scheme defined over $\mathbb{Z}$ and $K$ varies over all number fields. Under certain conditions, we show that these…

In recent work with Bober, Booker, Lee, Seymour-Howell, and Zubrilina, we proved murmuration behavior for Maass forms in the eigenvalue aspect and for modular forms in the weight aspect. Both used an approach based on the Selberg trace…

The ergodic theory and geometry of the Julia set of meromorphic functions on the complex plane with polynomial Schwarzian derivative is investigated under the condition that the forward trajectory of asymptotic values in the Julia set is…

We develop a new technique for proving concentration inequalities which relate between the variance and influences of Boolean functions. Using this technique, we 1. Settle a conjecture of Talagrand [Tal97] proving that $$\int_{\left\{…

We analyse the Multiplicative Anomaly (MA) in the case of quantized massive fermions coupled to a background torsion. The one-loop Effective Action (EA) can be expressed in terms of the logarithm of determinant of the appropriate…

Let $\mathscr{C}_n=\{-1,1\}^n$ be the discrete hypercube equipped with the uniform probability measure $\sigma_n$. Talagrand's influence inequality (1994) asserts that there exists $C\in(0,\infty)$ such that for every $n\in\mathbb{N}$,…