Related papers: On the Cheltsov--Rubinstein conjecture
It was shown by Bishop that if Thurston's $K = 2$ conjecture holds for some planar domain, then Brennan's conjecture holds for the Riemann map of that domain as well. In this paper we show numerically that the original counterexample to…
In this paper we propose generalizations of the Sokolov-Ternov and Unruh effects, and discuss the possibility to measure them on different experiments.
We prove Stanley's plethysm conjecture for the $2 \times n$ case, which composed with the work of Black and List provides another proof of Foulkes conjecture for the $2 \times n$ case. We also show that the way Stanley formulated his…
In the present note a generalization of Borel-Cantelli Lemma is proposed.
We generalize the toric residue mirror conjecture of Batyrev and Materov to not necessarily reflexive polytopes. Using this generalization we prove the toric residue mirror conjecture for Calabi-Yau complete intersections in Gorenstein…
There is a relation between the generalized Property R Conjecture and the Schoenflies Conjecture that suggests a new line of attack on the latter. The approach gives a quick proof of the genus 2 Schoenflies Conjecture and suffices to prove…
We give a new formula for the Littlewood--Richardson coefficients in terms of peelable tableaux compatible with shuffle tableaux, in the same fashion as Remmel--Whitney rule. This gives an efficient way to compute generalized…
We construct a finitely generated group that does not satisfy the generalized Burghelea conjecture.
One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these…
The aim of this work is to prove a conjecture related to the Combinatorial Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting, for lower intervals in every arbitrary Coxeter group. This result improves and…
We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the…
In this paper, we proved a special case of the DDVV Conjecture.
We develop the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular $L$-functions using multiple Dirichlet series under the generalized Riemann…
We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type…
The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.
We present simple randomized and exchangeable improvements of Markov's inequality, as well as Chebyshev's inequality and Chernoff bounds. Our variants are never worse and typically strictly more powerful than the original inequalities. The…
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new…