相关论文: Some recent progress on the Restriction conjecture

We survey recent results on Calderon's inverse problem with partial data, focusing on three and higher dimensions.

In this short note we give counterexamples to several results related to extension theorems published recently.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

A review of recent developments in the analyses of supersymmetric dark matter is given.

We recently formulated important Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Modular Johnson-Lindenstrauss Flattening Conjecture in the Appendix of \textit{[arXiv: 2207.12799.v1]}. For the sake of wide accessibility…

The purpose of this article is to survey the developments on the Kakeya problem in recent years, concentrating on the period after the excellent 1999 survey of Wolff, and including some recent work by the authors. We will focus on the…

Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix and consider an extension of it.

We propose to study the restriction conjecture using decoupling theorems and two-ends Furstenberg inequalities. Specifically, we pose a two-ends Furstenberg conjecture, which implies the restriction conjecture. As evidence, we prove this…

Recent developments in Seiberg-Witten theory and relations with Complex Geometry.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

We review some recent developments in the theory of $W_\infty$. We comment on its relevance to lower-dimensional string theory.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

Over the past few months, the theory of QCD at high density has been advanced considerably. It provides new perspectives on, and controlled realizations of, confinement and chiral symmetry breaking. Here I survey the recent developments,…

We review our construction of the Teichm\"uller TQFT. We recall our volume conjecture for this TQFT and the examples for which this conjecture has been established. We end the paper with a brief review of our new formulation of the…

This article gives an overview, aimed at theoretical particle physicists, of some recent developments in cosmology.

We survey recent progress in the theory of weak containment of measure preserving group actions.

We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.

Recent years have seen dramatic progress in cosmology and particle astrophysics. So much so that anyone who dares to offer an overview would certainly risk him- or herself for being incomplete and biased at best, and even incorrect due to…

We survey the classical results of the Dirichlet Approximation Theorem.

We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.