Related papers: A note on a recent attempt to prove Sendov's conje…
This is a survey paper of the developments on the geometric Bogomolov conjecture. We explain the recent results by the author as well as previous works concerning the conjecture. This paper also includes an introduction to the height theory…
This paper has been withdrawn by the authors due to an error in the proof of Lemma 3.9. The correct proof of global stability is given in arXiv:1101.5177
This paper has been withdrawn by the authors due to an error in Section 7.
In this small note we correct an error made by Mohammadi et al. in their paper entitled "On Skew Cyclic Codes Over A Finite Ring" ( Iranian Jl. Math. Sci. Inform. Vol 14 (1) (2019), 135-145).
We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.
In this note, we prove the magnetic spectral gap-labelling conjecture as stated in [arXiv:1508.01064], in all dimensions, for principal solenoidal tori.
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
There is a serious problem with one of the assumptions made in the security proof of the SURF scheme. This problem turns out to be easy in the regime of parameters needed for the SURF scheme to work. We give afterwards the old version of…
The SOM algorithm is very astonishing. On the one hand, it is very simple to write down and to simulate, its practical properties are clear and easy to observe. But, on the other hand, its theoretical properties still remain without proof…
In this note we present a collection of attempts of some researchers to prove or disprove whether the Zeraoulia sequences convergent. Even nowdays convergence of Zeraoulia sequences still open.
We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.
In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here we…
In this part, we prove several quantitative results concerning with the Szego minimum problem for classes of measure on the unit circle concentrated on small subsets. As a by-product, we refute one conjecture of Nevai. This note can be read…
In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].
This paper re-organizes Vojta's proof of the Mordell conjecture (i.e. Faltings' theorem) in terms of Arakelov geometry. A new ingredient is to replace an application of Gillet--Soule's arithmetic Riemannn--Roch theorem by that of Yuan's…
This note was written in Jan. 23, 2015 to answer a problem raised by G. Moser, who asked a constructive proof of a theorem by Ferreira-Zantema.
We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.
Remarkable progress has been made in recent years to establish log-Sobolev type inequalities under the assumption of discrete Ricci curvature bounds. More specfically, Salez and Youssef have proven that the log-Sobolev constant can be lower…
In this paper, we prove a conjecture by Daniele Mundici on the sum of squared distances between consecutive elements in the $Q$-th Farey sequence for $Q\in\mathbb{Z}$ and $Q\geq 2$.
We prove non-archimedean analogue of Sendov's conjecure. We also provide complete list of polynomials over an algebraically closed non-archimedean field $K$ that satisfy the optimal bound in the Sendov's conjecture.