Related papers: Singular integrals along lacunary directions in $\…

We describe the closures of locally divergent orbitsunder the action of tori on Hilbert modular spaces of rank r = 2. In particular, we prove that if D is a maximal R-split torus acting on a real Hilbert modular space then every locally…

The paper is centered around a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert-Einstein functional on the space of "warped polyhedra" with a fixed metric on the…

We give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in $\mathbb{C}^2$. We recall some classical obstructions and prove some deeper ones related to symplectic…

We prove a number of results relating various measures (volume, Legendrian index, stability index, and spectral curve genus) of the geometric complexity of special Lagrangian $T^2$-cones. We explain how these results fit into a program to…

We show that if $f$ is locally in $L\log\log L$ then the lacunary spherical means converge almost everywhere. The argument given here is a model case for more general results on singular maximal functions and Radon transforms (see ref. 6).

A periodic homogenization result of nonconvex integral functionals in the vectorial case with convex bounded constraints on gradients is proved. The class of integrands considered have singular behavior near the boundary of the convex set…

In this paper, we establish upper bounds on the dimension of sets of singular-on-average and \(\omega\)-singular affine forms in singly metric settings, where either the matrix or the shift is fixed. These results partially address open…

This paper present an overview of some of the applications of the martingale inequalities of D.L. Burkholder to $L^p$-bounds for singular integral operators, concentrating on the Hilbert transform, first and second order Riesz transforms,…

We survey recent work and announce new results concerning two singular integral operators whose kernels are holomorphic functions of the output variable, specifically the Cauchy-Leray integral and the Cauchy-Szeg\H o projection associated…

We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a $2n$-dimensional manifold. In the $\mathbb C$-analytic category this set consists of the Martinet hypersurface…

Notable results on the special values of $L$-functions of Siegel modular forms were obtained by J. Sturm in the case when the degree $n$ is even and the weight $k$ is an integer. In this paper we extend this method to half-integer weights…

We initiate the study of the $\ell^p(\mathbb{Z}^d)$-boundedness of the arithmetic spherical maximal function over sparse sequences. We state a folklore conjecture for lacunary sequences, a key example of Zienkiewicz and prove new bounds for…

We establish $L^2$ boundedness of all "nice" parabolic singular integrals on "Good Parabolic Graphs", aka {\em regular} Lip(1,1/2) graphs. The novelty here is that we include non-homogeneous kernels, which are relevant to the theory of…

We generalize Khintchine's method of constructing totally irrational singular vectors and linear forms. The main result of the paper shows existence of totally irrational vectors and linear forms with large uniform Diophantine exponents on…

We introduce and analyse infinite dimensional Wishart processes taking values in the cone $S^+_1(H)$ of positive self-adjoint trace class operators on a separable real Hilbert space $H$. Our main result gives necessary and sufficient…

This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…

Following I. S. Krasilshchik and A. M. Vinogradov, we regard PDEs as infinite-dimensional manifolds with involutive distributions and consider their special morphisms called differential coverings, which include constructions like Lax pairs…

The fact that each finite-dimensional algebra over a field is isomorphic to the centralizer of two matrices, has suggested to investigate representation theoretical problems of finite-dimensional algebras through centralizer algebras of…

This text presents several aspects of the theory of equisingularity of complex analytic spaces from the standpoint of Whitney conditions. The goal is to describe from the geometrical, topological, and algebraic viewpoints a canonical…

Let $T$ be a triangulation of a Riemann surface. We show that the 1-skeleton of $T$ may be oriented so that there is a global bound on the outdegree of the vertices. Our application is to construct extremal metrics on triangulations formed…