Related papers: Some recent progress on the Restriction conjecture
We update and extend our previous work reconstructing the potential of a quintessence field from current observational data. We extend the cosmological dataset to include new supernova data, plus information from the cosmic microwave…
I briefly review the numerical evidence, some old and some quite recent, in favor of the center vortex theory of confinement.
This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.
We review selected recent theoretical activity in perturbative QCD. We focus on progress in the description of parton densities, including latest developments in neural network parton densities, on the description of high multiplicity final…
In this paper we consider the remaining cases of Hebey-Vaugon conjecture.
We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.
This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
There have been many remarkable developments in our understanding of superstring theory in the past few years, a period that has been described as ``the second superstring revolution.'' Several of them are discussed here. The presentation…
We present a short review of the existing evidence in favor of neutrino mass and neutrino oscillations which come from different kinds of experiments. We focus our attention in particular on solar neutrinos, presenting a global updated…
Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…
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…
We establish some new theorems on pentagon and pentagram.
An overview of last seven years results concerning Sarnak's conjecture on M\"obius disjointness is presented, focusing on ergodic theory aspects of the conjecture.
We attempt to prove the Razumov-Stroganov conjecture using a bijectional approach. We have been unsuccessful but we believe the techniques we present can be used to prove the conjecture.
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…
We introduce two families of inequalities. Large ensemble decoupling is connected to the continuous restriction phenomenon. Tight decoupling is connected to the discrete Restriction conjecture for the sphere. Our investigation opens new…
We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…
We give a survey of various compactness and non-compactness results for the Yamabe equation. We also discuss a conjecture of Hamilton concerning the asymptotic behavior of the parabolic Yamabe flow.