相关论文: Recent progress on the Kakeya conjecture
Physicists have pondered the origin of cosmic rays for over a hundred years. However the last few years have seen an upsurge in the observation, progress in the theory and a genuine increase in the importance attached to the topic due to…
In this paper, we will continue the investigation of Waring's problem, and give further improvements.
This article is a brief introduction to the rapidly evolving field of many-body localization. Rather than giving an in-depth review of the subject, our aspiration here is simply to introduce the problem and its general context, outlining a…
The Fourier restriction phenomenon and the size of Kakeya sets are explored in the setting of the ring of integers modulo $N$ for general $N$ and a striking similarity with the corresponding euclidean problems is observed. One should…
We survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles for equivariant isomorphisms of Stein manifolds on which a reductive complex Lie group $G$…
An overview is given on recent developments in the affine Weyl group approach to Painlev\'e equations and discrete Painlev\'e equations, based on the joint work with Y. Yamada and K. Kajiwara.
A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered
This paper forms part of a long-term project to put field electron emission (FE) onto a better scientific basis, by seeking reliable quantitative agreement between theory and experiment, especially as regards emission-current values. The…
This is a survey article, to appear in the Proceedings of the 2018 International Congress of Mathematicians. (Revised, with added and updated references.)
This survey aims to give an overview of several substantial developments of the last 50 years in the structure theory of regular semigroups and to shed light on their impact on other parts of semigroup theory.
This article gives an overview, aimed at theoretical particle physicists, of some recent developments in cosmology.
A conjectural generalization of the McKay correspondence in terms of stringy invariants to arbitrary characteristic, including the wild case, was recently formulated by the author in the case where the given finite group linearly acts on an…
Recent results by space borne experiments took cosmic ray data to a precision level. These new results are able to challenge the conventional scenario for cosmic ray acceleration and propagation in the Milky Way. In these contributions,…
At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two…
I provide a short review of the current status of indirect dark matter searches with gamma rays, charged cosmic rays and neutrinos. For each case I will focus on various excesses reported in the literature which have been interpreted as…
We overview a web of conjectures about torsors under reductive groups over regular rings and survey some techniques that have been used for making progress on such problems.
We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.
In this note, we use recent advances concerning the K-stability of $\mathbb{Q}$-Fano varieties to provide settings for which Vojta's conjecture holds.
The method of higher covariant derivative regularization of gauge theories is reviewed. The objections raised in the literature last years are discussed and the consistency of the method is proven. New approach to regularization of…
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.