Related papers: Recent progress on the Kakeya conjecture
I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…
I review recent theoretical advances in quantum chromodynamics. Particular emphasis is put on developments related to the precise prediction and interpretation of experimental data from present and future high energy colliders.
This is an expository paper. We give proofs of some results of M. Christ (1984) and S. W. Drury (1984) for $k$-plane transforms. Also, we give proofs for some related results including that for the existence of invariant measures on certain…
The last decade has been dense with new developments in the search for the sources of Galactic cosmic rays. Some of these developments have confirmed the tight connection between cosmic rays and supernovae in our Galaxy, through the…
The work is devoted to the critical analysis of theoretical prediction and astronomical observation of GR effects, first of all, the Mercury's perihelion advance. In the first part, the methodological issues of observations are discussed…
The search for the origin of cosmic rays is as active as ever, mainly driven by new insights provided by recent pieces of observation. Much effort is being channelled in putting the so called supernova paradigm for the origin of galactic…
We survey some recent development in the stability theory of klt singularities. The main focus is on the solution of the stable degeneration conjecture.
This article serves as an introduction to the linear aspects of the recent submission by Krieger, Miao, and the author, see arXiv:2009.08843. It also surveys some of the results obtained on the decay of linear waves on various backgrounds…
We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao.
In the finite field setting, we show that the restriction conjecture associated to any one of a large family of $d=2n+1$ dimensional quadratic surfaces implies the $n+1$ dimensional Kakeya conjecture (Dvir's theorem). This includes the case…
This is a survey paper of the developments on the geometric Bogomolov conjecture. We explain the recent results by the author as well as previous works concerning the conjecture. This paper also includes an introduction to the height theory…
The past few years have seen several breakthroughs in particle astrophysics and cosmology. In several cases, new observations can only be explained with the introduction of new fundamental physics. In this talk I summarize some of these…
Let $L$ be a set of lines of an affine space over a field and let $S$ be a set of points with the property that every line of $L$ is incident with at least $N$ points of $S$. Let $D$ be the set of directions of the lines of $L$ considered…
The general features of the cosmic-ray spectrum have been known for a long time. Although the basic approaches to understanding cosmic-ray propagation and acceleration have also been well understood for many years, there are several…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…
The purpose of this short paper is to investigate relations between various real K-theories. In particular, we show how a real projective bundle theorem implies an unexpected relation between Atiyah's KR-theory and the usual equivariant…
Since 1968, when the Golomb--Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although there is a vast literature on the topic and it is widely believed to be true,…
We give new lower bounds for the Hausdorff dimension of Kakeya sets built from various families of curves in $\mathbb R^3$, going beyond what the polynomial partitioning method has so-far achieved. We do this by combining Wolff's classical…