Related papers: On a conjecture by Blocki-Zwonek

We prove a conjecture of Johann Cigler on shifted Hankel determinants.

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

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

We give a counterexample to a conjecture posed by S. Ding regarding the index of a Gorenstein local ring by exhibiting several examples of one dimensional local complete intersections of embedding dimension three with index 5 and…

This paper contains the proof of difference counterparts of the conjectures due to Keven Kadell on symmetric and anti-symmetric Macdonald polynomials.

The aim of this note is to show that the local form of the logarithmic Brunn-Minkowski conjecture holds for zonoids. The proof uses a variant of the Bochner method due to Shenfeld and the author.

A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems…

This is an introduction to Taubes's proof of the Weinstein conjecture, written for the AMS Current Events Bulletin. It is intended to be accessible to nonspecialists, so much of the article is devoted to background and context.

In this paper we give an example to show Clemens' conjecture is not a first order deformation problem.

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.

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

In this paper the circulant Hadamard conjecture is proved.

In this note we give a counter example to a conjecture of Malle which predicts the asymptotic behaviour of the counting functions for field extensions with given Galois group and bounded discriminant.

A generalization of Young's inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified…

In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. We explore special cases of this conjecture and present supporting evidence. In particular we…

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered

We disprove a conjecture of Kuznetsov--Shinder, which posits that $D$-equivalent simply connected varieties are $L$-equivalent, by constructing a counterexample using moduli spaces of sheaves on K3 surfaces.

One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.