Related papers: Recent progress on the Kakeya conjecture
I review in a schematic way the current status of indirect searches for Dark Matter: I list the main relevant experimental results of the recent years and I discuss the excitements and disappointments that their phenomenological…
This paper surveys some of our recent progress on Hardy-type inequa\-lities which consist of a well-known topic in Harmonic Analysis. In the first section, we recall the original probabilistic motivation dealing with the stability speed in…
Over the last decade, cosmological observations have attained a level of precision which allows for detailed comparison with theoretical predictions. In this paper, we briefly review some studies of the current and prospected constraints…
In This paper, we survey recent progress on the theory of Gromov- Witten invariants on Hilbert schemes of points mainly on elliptic surfaces and simply connected minimal surface of general type. In particular, we focus on the aspects of…
This is an informal survey of progress in Weihrauch complexity (cf arXiv:1707.03202) in the period 2018-2020. Open questions are emphasised.
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
We prove a bilinear Kakeya inequality in the first Heisenberg group and a sharp bilinear Kakeya estimate for Euclidean curved tubes in $\R^2$. By adapting an argument of F\"assler, Pinamonti and Wald involving Heisenberg projections, we…
Some highlights of the recent researches in the field of relativistic jets are reviewed and critically analyzed. Given the extent of the available literature, this essay symbolically takes the baton from the outstanding and recent review by…
Fundamental spin physics has made striking progresses in the last years; new ideas, experiments and data interpretations have been proposed and keep emerging. A review of some of the most important issues in the spin structure of nucleons…
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
Efforts to understand and map the possible explanations for the late time acceleration of the universe have led to a broad range of suggestions, ranging from the cosmological constant and straightforward dark energy, to exotically coupled…
Let $\mathcal{L}$ be a family of lines and let $\mathcal{P}$ be a family of $k$-planes in $\mathbb{F}^n$ where $\mathbb{F}$ is a field. In our first result we show that the number of joints formed by a $k$-plane in $\mathcal{P}$ together…
Studies of galaxy evolution at optical and near-infrared wavelengths have reached an interesting point in their historical development and the arrival of a new millenium provides an appropriate occasion to review the overall direction in…
We show that the problem of counting collinear points in a permutation (previously considered by the author and J. Solymosi in "Collinear Points in Permutations", 2005) and the well-known finite plane Kakeya problem are intimately…
This is a rough write-up of my lecture at Kinosaki and two lectures at RIMS workshops in Dec 1996, on work in progress that has not yet reached any really worthwhile conclusion, but contains lots of fun calculations. History of Vafa's…
This thesis investigates two problems that are discrete analogues of two harmonic analytic problems which lie in the heart of research in the field. More specifically, we consider discrete analogues of the maximal Kakeya operator conjecture…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.
We provide an alternative and self contained proof of the main result of Bennett, Carbery, Tao regarding the multilinear restriction estimate. The approach is inspired by the recent result of Guth about the Kakeya version of multilinear…
Direct techniques for cosmic ray observations have reached an unprecedented level of precision, unveiling fine-details of the energy spectra. I will introduce the evidence for new spectral features which has been accumulated by new…