Related papers: A note on the Stein restriction conjecture and the…

We present a restriction theorem for the Fourier transform to a 2-dimensional conical surface of finite type, obtaining a sharp result, which improves previous work by Barcelo.

We generalize our method for subconvex bounds for $\mathrm{GL}_2 \times \mathrm{GL}_1$ to the setting of the Waldspurger's formula for compact torical integrals. We address the two major difficulties: one is the lack of split places with…

We improve the range for the discrete Fourier restriction to the four and five dimensional spheres. We rely on two new ingredients, incidence theory and Siegel's mass formula.

Recently Wolff obtained a nearly sharp $L^2$ bilinear restriction theorem for bounded subsets of the cone in general dimension. We obtain the endpoint of Wolff's estimate and generalize to the case when one of the subsets is large. As a…

Mockenhaupt and Tao (Duke 2004) proved a finite field analogue of the Stein--Tomas restriction theorem, establishing a range of $q$ for which $L^q\to L^2$ restriction estimates hold for a given measure $\mu$ on a vector space over a finite…

We propose a new approach to the question of prescribing Gaussian curvature on the 2-sphere with at least three conical singularities and angles less than $2\pi$, the main result being sufficient conditions for a positive function of class…

Let E be a stable rank 2 vector bundle on a smooth quadric threefold Q in the projective 4-space P. We show that the hyperplanes H in P for which the restriction of E to the hyperplane section of Q by H is not stable form, in general, a…

We look into the general aspects of space-time symmetries in presence of torsion, and how the latter is affected by such symmetries. Focusing in particular to space-times which either exhibit maximal symmetry on their own, or could be…

In this paper we introduce a new type of restriction problem, called the \textit{restriction problem with moments}. We show that the surface area measure of the sphere satisfies the $L^p$-$L^2$ restriction problem with moments if $1 \leq p…

Let $n$, $k$, and $t$ be integers satisfying $n>k>t\ge2$. A Steiner system with parameters $t$, $k$, and $n$ is a $k$-uniform hypergraph on $n$ vertices in which every set of $t$ distinct vertices is contained in exactly one edge. An…

A Steinhaus set $S \subseteq \RR^d$ for a set $A \subseteq \RR^d$ is a set such that $S$ has exactly one point in common with $\tau A$, for every rigid motion $\tau$ of $\RR^d$. We show here that if $A$ is a finite set of at least two…

The famous Stein-Weiss inequality on $\mathbf R^n \times \mathbf R^n$, also known as the doubly weighted Hardy-Littlewood-Sobolev inequality, asserts that \[ \Big| \iint_{\mathbf R^n \times \mathbf R^n} \frac{f(x) g(y)}{|x|^\alpha…

We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…

Seiberg-Witten theory is used to obtain new obstructions to the existence of Einstein metrics on 4-manifolds with conical singularities along an embedded surface. In the present article, the cone angle is required to be of the form 2(pi)/p,…

We consider a suspension of spherical inertialess particles in a Stokes flow on the torus $\mathbb T^3$. The particles perturb a linear extensional flow due to their rigidity constraint. Due to the singular nature of this perturbation, no…

We study the decision version of tensor spectral norm from the viewpoint of real algebraic complexity. For a rationally specified tensor, the tensor spectral threshold problem asks whether its spectral norm exceeds a prescribed rational…

We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system in bounded domains, in two dimensions, with Dirichlet boundary conditions for the Navier-Stokes and Poisson equations, and blocking (vanishing…

In this paper, we introduce a notion of stable coarse algebras for metric spaces with bounded geometry, and formulate the twisted coarse Baum--Connes conjecture with respect to stable coarse algebras. We prove permanence properties of this…

A Stein operator for the runs is derived as a perturbation of an operator for discrete Gibbs measure. Due to this fact, using perturbation technique, the approximation results for runs arising from identical and non-identical Bernoulli…

We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approach introduced by Agrachev and Sarychev.…