Related papers: On the DDVV Conjecture and the Comass in Calibrate…
We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…
We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…
General considerations on the Equivalence conjectures and a review of few mathematical results.
Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as the quintic 3-fold. By two different wall-crossing arguments we prove two different explicit formulae relating rank 0 Donaldson-Thomas…
A new construction, with more visible canonical features, of a qKdV equation in a q-Virasoro context is exhibited.
In ["Illumination of convex bodies with many symmetries", Mathematika 63 (2017)], Tikhomirov verified the Hadwiger-Boltyanski Illumination Conjecture for the class of 1-symmetric convex bodies of sufficiently large dimension. We propose an…
In this paper we consider the remaining cases of Hebey-Vaugon conjecture.
In this paper, we prove a conjecture of Schnell in the surface case.
In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…
In this paper, we give a survey on the history and recent developments on the DDVV-type inequalities.
We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
We prove that isometries in a conformally invariant metric of a general domain are quasiconformal. In the particular case of the punctured space, we prove that isometries in this metric are Mobius, thus resolving a conjecture of Ferrand,…
In this paper we give a proof of the Manickam-Mikl\'os-Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, several specific…
We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
The paper presents a counterexample to the Hodge conjecture.
We prove the Strong Jacobi Bound Conjecture for generically reduced components of differential schemes.
In this paper, we prove some new inequalities of Hadamard-type for convex functions on the co-ordinates.
This is a short essay about some fundamental results on scalar curvature and the two key methods that are used to establish them.
We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected…