Related papers: Summary on the proof of BAB Conjecture
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
We survey recent developments on the Restriction conjecture.
This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.
We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The…
A proof of Smale's mean value conjecture from 1981 is given.
This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.
In this paper, we prove a conjecture of Schnell in the surface case.
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
We prove the Aharoni Berger Conjecture
We present the proofs of the conjectures mentioned in the paper published in the proceedings of the 2024 AAAI conference [1], and discovered by the decomposition methods presented in the same paper.
We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
This is a survey on Kawaguchi-Silverman conjecture.
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…
We discuss the validity of the proof of the fixed numerator conjecture on Markov numbers, which is the main result of the paper mentioned in the title.
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.
In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.
In this mostly expository note, we explain a proof of Tate's two conjectures [Tat65] for algebraic cycles of arbitrary codimension on certain products of elliptic curves and abelian surfaces over number fields.
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.