相关论文: Recent progress on the Kakeya conjecture

One of the great endeavors of the past decade has been the evaluation of different observational techniques for measuring dark energy properties and of theoretical techniques for constraining models of cosmic acceleration given cosmological…

Numerical relativity has come a long way in the last three decades and is now reaching a state of maturity. We are gaining a deeper understanding of the fundamental theoretical issues related to the field, from the well posedness of the…

We consider the physics motivations and perspectives for the study of spin phenomena at the future high energies accelerators. The possibilities to use the already operating machines are also discussed. It is emphasized that the present…

The paper is a short survey of recent developments in the area of word maps evaluated on groups and algebras. It is aimed to pose questions relevant to Kac--Moody theory.

Upcoming and planned experiments combining increasingly intense lasers and energetic particle beams will access new regimes of nonlinear, relativistic, quantum effects. This improved experimental capability has driven substantial progress…

In this short note we briefly review some recent developments in understanding discrete torsion. Specifically, we give a short overview of the highlights of a group of recent papers which give the basic understanding of discrete torsion.…

Inspired Yau's work (Comm. Anal. Geom., 1994), in this short note we provide a new version of Li-Yau gradient estimate for the linear heat equation, which generalizes some known results and gives new gradient estimates. Also we explain the…

This is a survey about recent progress in Rankin-Cohen deformations. We explain a connection between Rankin-Cohen brackets and higher order Hankel forms.

The locality hypothesis is generally considered necessary for the study of the kinematics of non-inertial systems in special relativity. In this paper we discuss this hypothesis, showing the necessity of an improvement, in order to get a…

We give an overview of ongoing searches for effects motivated by the study of the quantum-gravity problem. We describe in greater detail approaches which have not been covered in recent ``Quantum Gravity Phenomenology'' reviews. In…

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

An overview is given on the present status of the understanding of the origin of galactic cosmic rays. Recent measurements of charged cosmic rays and photons are reviewed. Their impact on the contemporary knowledge about the sources and…

The discovery and subsequent study of microquasars lead to major progress in our understanding of: 1) the nature of relativistic jets seen elsewhere in the universe, and 2) the connection between the accretion onto compact objects and the…

Numerous research studies have been investigated on proxy signatures over the last decade. This survey reviews the research progress on proxy signatures, analyzes a few notable proposals, and provides an overall remark of these proposals.

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

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…

Current phenomenological studies of jet observables at colliders are clearly limited by the theoretical uncertainties inherent in the next-to-leading order QCD description. We discuss the recent progress made towards the calculation of QCD…

We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level…

Hurwitz spaces which parametrize branched covers of the line play a prominent role in inverse Galois theory. This paper surveys fifty years of works in this direction with emphasis on recent advances. Based on the Riemann-Hurwitz theory of…

This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspects of Tverberg's theorem and its applications. The survey…