Related papers: A note on the Artin Conjecture
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.
In this article we survey some of the recent developments in the structure theory of set addition.
A conjecture regarding the structure of expander graphs is discussed.
Dual presentations of Coxeter groups have recently led to breakthroughs in our understanding of affine Artin groups. In particular, they led to the proof of the $K(\pi, 1)$ conjecture and to the solution of the word problem. Will the "dual…
The present note sketches a theory of constructs.
We survey the classical results of the Dirichlet Approximation Theorem.
This article is about Artin's braid group and its role in knot theory. We set ourselves two goals: (i) to provide enough of the essential background so that our review would be accessible to graduate students, and (ii) to focus on those…
This is an exposition on the General Neron Desingularization and its applications. We end with a recent constructive form of this desingularization in dimension one
We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
In this paper we prove the WALA conjecture.
In this mostly expository note we explain how Nori's theory of motives achieves the aim of establishing a Galois theory of periods, at least under the period conjecture. We explain and compare different notions periods, different versions…
Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
Abstract. We address the conjecture which states that an intersection of parabolic subgroups of an Artin-Tits group is a parabolic subgroup. We prove that the conjecture is equivalent to a, a priori, weaker conjecture. We also prove the…
We survey some old and new results on strong variants of Chang's Conjecture and related topics.
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.
An overview of the recent developments in plurifine potential theory.
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.