Related papers: The magic of 8 and 24
A close look of Google's GNoME inorganic materials dataset [Nature 624, 80 (2023)], and 11 things you would like to know.
GGR News: - Remembering Wheeler, by Jim Isenberg; Research Briefs: - A Brief Summary of the WMAP5 Results, by Lyman Page; - Science with LIGO, by Maria Alessandra Papa; Conference Reports: - 7th LISA Symposium, by Edward K. Porter; - The…
We generalize the recent work of Viazovska by constructing infinite families of Schwartz functions, suitable for Cohn-Elkies style linear programming bounds, using quasi-modular and modular forms. In particular for dimensions $d \equiv 0…
This text, on the one hand, is related to the talk delivered at the Conference "Gauge Fields. Yesterday, Today, Tomorrow", dedicated to the Andrej Slavnov 70th anniversary; on the other - in the form of a fairy tale - it summarizes some…
This is a Snowmass whitepaper on physical mathematics. It briefly summarizes and highlights some of the key questions drawn from a much more extensive essay, by the same authors, entitled, "A Panorama Of Physical Mathematics 2021."
This is a manuscript accepted for publication on Physical Review Fluids, Gallery of Fluid Motion special issue. The manuscript is associated with a poster winner of the 39th Annual Gallery of Fluid Motion Award, for work presented at the…
Andrei Okounkov received the Fields Medal at the ICM 2006 in Madrid "for his contributions bridging probability, representation theory and algebraic geometry". This is a brief account of his work.
These are the preparatory notes for a Science & Music essay, "Playing by numbers", appeared in Nature 453 (2008) 988-989.
We provide the problems and their solutions to the 2020 USA Mathematical Olympiad.
This is an overview of some of the works of Avi Wigderson, 2021 Abel prize laureate. Wigderson's contributions span many fields of computer science and mathematics. In this survey we focus on four subfields: cryptography, pseudorandomness,…
This article contains the introduction to the special volume of Stochastics dedicated to Priscilla Greenwood, her CV and her list of publications.
About twenty years ago, Green wrote a survey article on the utility of looking at toy versions over finite fields of problems in additive combinatorics. This article was extremely influential, and the rapid development of additive…
This technical report accompanies the following three papers. It contains the computations necessary to verify some of the results claimed in those papers. [1] Carolyn Chun, Deborah Chun, Dillon Mayhew, and Stefan H. M. van Zwam.…
After a long qualifying process packed with surprises (Italy missing out as the reigning European champions) and last minute drama (both Egypt and Peru missed out on penalties), the FIFA World Cup 2022 kicked off on the 20th of November in…
A Comment on the Letter by Atsushi Ikeda and Kunimasa Miyazaki, [arXiv:1003.5472v2, Phys. Rev. Lett. 104, 255704 (2010)].
Suppose some cleverness score parameter is sufficiently interesting to be defined and then measured, perhaps for different strata of specialists or for the broader population. Such phenomena could have Gaussian distributions, when it comes…
Parity games are positionally determined. This is a fundamental and classical result. In 2010, Calude et al. showed a breakthrough result for finite parity games: the winning regions and their positional winning strategies can be computed…
Suppose $\mathbb{F}$ is a field and let $\mathbf{a} := (a_1, a_2, \dotsc)$ be a sequence of non-zero elements in $\mathbb{F}$. For $\mathbf{a}_n := (a_1, \dotsc, a_n)$, we consider the family $\mathcal{M}_n(\mathbf{a})$ of $n \times n$…
The content of this paper is now available as part of arXiv:0802.2019
What is an interesting number theoretic or a combinatorial characterization of the divisors of 24 amongst all positive integers? In this paper I will provide one characterization in terms of modular multiplication tables. This idea evolved…