Related papers: On two recent conjectures in convex geometry

We prove a conjecture of Roe by constructing unified warped cones that violate the coarse Baum-Connes conjecture. Interestingly, the reason for this is probably not what Roe expected, as the obstruction arises in odd rather than even…

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 short note we prove by a counter-example that Theorem 3.2 in the paper "A study on concave optimization via canonical dual function" by J. Zhu, S. Tao, D. Gao is false; moreover, we give a very short proof for Theorem 3.1 in the…

We show that the Jacobian conjecture of the two dimensional case is true.

The volume conjecture, formulated recently by H. Murakami and J. Murakami, is proved for the case of torus knots.

We give a brief proof of a recent result of Avron, Seiler and Simon.

We construct a simple acyclic directed graph for which the Bunkbed Conjecture is false, thereby resolving conjectures posed by Leander and by Hollom.

Nous refutons, sous une certaine hypothese combinatoire, la "nonrevisiting path conjecture". Abstract: In this article, we give, under some hypothesis, a couterexample to the nonrevisiting path conjecture.

In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873], using a method for proving inequalities of mixed trigonometric polynomial functions.

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

This paper has been withdrawn by the author due a crucial sign error in Theorem B. We present a geometric proof of Thom conjecture, which uses Khovanov homology. Our approach doesn't use any analytic methods and is quite different from…

We discuss various phenomena of tangency in projective and convex geometry.

The Sharpened Distance Conjecture and Tower Scalar Weak Gravity Conjecture are closely related but distinct conjectures, neither one implying the other. Motivated by examples, I propose that both are consequences of two new conjectures: 1.…

Let F be a finite set of circles in the plane. We point out that the usual convex closure restricted to F yields a convex geometry, that is, a combinatorial structure introduced by P. H Edelman in 1980 under the name "anti-exchange closure…

Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…

The purpose of this note is to show by constructing counterexamples that two conjectures of M\'{o}ri and Sz\'{e}kely for the Borel-Cantelli lemma are false.

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.

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

W. M. Hirsch formulated a beautiful conjecture on diameters of convex polyhedra.I suggest a new viewpoint with the deformation and moduli of polytopes.

A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of K. Adaricheva and M. Bolat (2016) and the Polymath REU 2020 team, continues to investigate representations of convex geometries…