Related papers: On Arnold's and Pushkin's puzzles
Oleg Viro studied in arXiv:math/0204290 two interpretations of the (multivariable) Alexander polynomial as a quantum link invariant: either by considering the quasi triangular Hopf algebra associated to $U_q sl(2)$ at fourth roots of unity,…
Following the general strategy proposed by G.Rybnikov, we present a proof of his well-known result, that is, the existence of two arrangements of lines having the same combinatorial type, but non-isomorphic fundamental groups. To do so, the…
I respond to the Bernard et al. comment on my letter ``Chiral anomalies and rooted staggered fermions.''
The paper consists of two parts. The first part is devoted to logic for universal algebraic geometry. The second one deals with problems and some results. It may be regarded as a brief exposition of some ideas from the book in progress:…
We study analogues of Sidorenko's conjecture and the forcing conjecture in oriented graphs, showing that natural variants of these conjectures in directed graphs are equivalent to the asymmetric, undirected analogues of the conjectures.
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
We study variants of Sidorenko's conjecture in tournaments, where new phenomena arise that do not have clear analogues in the setting of undirected graphs. We first consider oriented graphs that are systematically under-represented in…
We describe the Wigner's-Friend scenario according to Wigner, then a similar but earlier version according to Everett. Wigner and Everett provide different resolutions of essentially the same paradox. Decoherence theory provides a third…
In this note we give some remarks and improvements on a recent paper of us [3] about an optimization problem for the $p-$Laplace operator that were motivated by some discussion the authors had with Prof. Cianchi.
This is the English translation of the short note where the first nontrivial tetrahedron relation (solution of the Zamolodchikov tetrahedron equation) with variables on the edges was presented.
The EPR (Einstein, Podolsky, Rosen) argument and the Schrodinger cat paradox are revisited in relation with modern quantum optics and atomic physics and with the concept of decoherence. It is shown that the questions raised fifty years ago…
These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.
In this paper, I review the book: Gary S. Berger, Michael DiRuggiero. "Einstein: The Man and His Mind." Bologna: Damiani, 2022. Illustrations. 209 pp. $70.00, cloth, ISBN 978-88-6208-784-1.
The two of us have shared a fascination with James Victor Uspensky's 1937 textbook $Introduction \, to \, Mathematical \, Probability$ ever since our graduate student days: it contains many interesting results not found in other books on…
This is a slightly modified version of my MSc thesis from 2019. Supervisor was D\"om\"ot\"or P\'alv\"olgyi.
This is a short note about a chapter in the author's bachelor thesis regarding a paper by Ford concerning a conjecture by Erd\H{o}s.
We give an informal introduction to the authors' work on some conjectures of Kazhdan and Lusztig, building on work of Soergel and de Cataldo-Migliorini. This article is an expanded version of a lecture given by the second author at the…
I will report below on a few examples of raving and insane (or maybe utterly genial) sentences that can be found in famous and otherwise admirable books of physics, because I genuinely believe it is amusing.
We introduce a superanalogue of the classical Markov equation. This equation characterizes the ``shadow Markov numbers'' recently considered by one of us. We show that this equation is characterized by invariance by cluster algebra…
New sequences of orthogonal polynomials with ultra-exponential weight functions are discovered. In particular, it gives an explicit solution to the Ditkin-Prudnikov problem (1966). The 3-term recurrence relations, explicit representations,…