Related papers: Recent progress on the Kakeya conjecture
The search for dark matter is a very wide and active field of research. Many potential hints of dark matter have appeared recently which led to a burst of theoretical activity and model building. I necessarily concentrate here only in some…
We review progress in high-energy cosmic ray physics focusing on recent experimental results and models developed for their interpretation. Emphasis is put on the propagation of charged cosmic rays, covering the whole range from $\sim…
The aim of this note is to provide a concise introduction to so-called problems of unlikely intersections for (pure) Shimura varieties and to review the current state-of-the-art. In the process, we will touch upon more general settings and…
This is a revision of my original posting, in which I raised objections to part of the Conway-Kochen argument. I now agree with them that their recent reply answers my original concerns. In the first part of these notes (identical to the…
We prove that if a circular arc has angle short enough, then it can be continuously moved to any prescribed position within a set of arbitrarily small area.
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
We prove the Kakeya set conjecture for $\mathbb{Z}/N\mathbb{Z}$ for general $N$ as stated by Hickman and Wright [HW18]. This entails extending and combining the techniques of Arsovski [Ars21a] for $N=p^k$ and the author and Dvir [DD21] for…
I review the recent theoretical progress towards the computation of jet observables at two loops in QCD.
By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…
Several complementary approaches to investigate knotted solutions of Maxwell's equations in vacuum are now available in literature. However, only partial results towards a unified description of them have been achieved. This is potentially…
The last two decades have brought spectacular advances in astrophysics of cosmic rays (CRs) and space- and ground-based astronomy. Launches of missions that employ forefront detector technologies enabled measurements with large effective…
Digital radio detection of cosmic rays has made tremendous progress over the past decade. It has become increasingly clear where the potential --- but also the limitations --- of the technique lie. In this article, we discuss roads that…
We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.
Kakeya sets are compact subsets of $\mathbb{R}^n$ that contain a unit line segment pointing in every direction. The Kakeya conjecture states that such sets must have Hausdorff dimension $n$. The property of stickiness was first discovered…
In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…
I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a…
The status of the electroweak Standard Model is reviewed in the light of recent precision data and new theoretical results which have contributed to improve the predictions for precision observables, together with the remaining inherent…
The paper is a short survey of recent developments in the area of first order descriptions of linear groups. It is aimed to illuminate the known results and to pose the new problems relevant to logical characterizations of Chevalley groups…
This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.
The aim of this survey paper is threefold: (a) to discuss the status of the Morrison-Kawamata cone conjecture, (b) to report on recent developments towards the Abundance Conjecture, and (c) to discuss the nef line bundle version of the…