相关论文: Recent progress on the Kakeya conjecture
In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…
A recent paper published in Am. J. Phys. describes an experiment designed to measure the one-way speed of light. Although the experiment is very interesting, in particular to be used in student laboratories, it is in fact determining the…
In this review, I discuss briefly theoretical scenarios concerning the interpretation of recent results from indirect and direct dark matter searches, with emphasis on the former.
Late-time cosmic acceleration is one of the most interesting unsolved puzzles in modern cosmology. The explanation most accepted nowadays, dark energy, raises questions about its own nature, e.g. what exactly is dark energy, and…
I review the progress in fundamental spin physics over the past several years and the prospects for the future. The progress is striking and the prospects are excellent.
The aim of this article is to provide a complementary understanding to some results of the second author using the machinery of Koszul complexes, and to explain how this approach can provide a new description of projective derived…
A Besicovitch set is a subset of $\R^d$ that contains a unit line segment in every direction and the famous Kakeya conjecture states that Besicovitch sets should have full dimension. We provide a number of results in support of this…
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.
Problems solved? Pulsar research must be considered - 35 years after the detection of pulsars - a mature science, where the basic questions have been raised and discussed. One would hope that many if not all generic and important problems…
In this letter a new formula for light deflection is derived using only physically observable concepts. The general result is specialized to cosmological perturbation theory and expressed in terms of gauge--invariant perturbation variables.…
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…
The paper is concerned with the development of a gravitational field theory having locally a covariant version of the Galilei group. We show that this Galilean gravity can be used to study the advance of perihelion of a planet, following in…
In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. We explore special cases of this conjecture and present supporting evidence. In particular we…
We survey the interconnections between geometric combinatorics (such as the Kakeya problem), arithmetic combinatorics (such as the classical problem of determining which sets contain arithmetic progressions), oscillatory integrals (such as…
The purpose of this paper is twofold: first we give a survey on the recent developments of curve counting invariants on Calabi-Yau 3-folds, e.g. Gromov-Witten theory, Donaldson-Thomas theory and Pandharipande-Thomas theory. Next we focus on…
Theories proposing a varying speed of light have recently been widely promoted under the claim that they offer an alternative way of solving the standard cosmological problems. Recent observational hints that the fine structure constant may…
After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond \Lambda, or smooth dark energy, often called…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
I will review the most recent and interesting results from gravitational wave detection experiments, concentrating on recent results from the LIGO Scientific Collaboration (LSC). I will outline the methodologies utilized in the searches,…