Related papers: Number Gossip
New cases of the multiplicity conjecture are considered.
We consider unknown ad-hoc radio networks, when the underlying network is bidirectional and nodes can have polynomially large labels. For this model, we present a deterministic protocol for gossiping which takes $O(n \lg^2 n \lg \lg n)$…
This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.
This article is a summary of eight of Jim Gray's transaction papers. It was written at the invitation of Pat Helland to be a chapter of a forthcoming book in the ACM Turing Award winners' series, "Curiosity, Clarity, and Caring: How Jim…
An overview of the ESO/Radionet workshop devoted to 3D optical/near-infrared and sub-mm/radio observations of gas and stars in galaxies is presented. There will be no published proceedings but presentations are available at…
This is an extended version of notes prepared for the talk at the conference "Rajchman-Zygmund-Marcinkiewicz 2000" based on recent works of the authors.
This update to my article on Congruent numbers, elliptic curves, and the passage from the local to the global, which appeared in Resonance, December 2009, pp. 1183--1205 (https://www.ias.ac.in/describe/article/reso/014/12/1183-1205) and was…
We use the results of AG/0406290 to discuss the counting formulas of network flow polytopes and magic squares, i.e. the formula for the corresponding Ehrhart polynomial in terms of residues. We also discuss a description of the big cells…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
Recent exact analytical results developed for the random number generators with taps are reported. These results are applicable to a wide class of algorithms, including random walks, cluster algorithms, Ising models. Practical…
These are notes based on a course that I gave at the University of Chicago in Fall 2016 on "Loop measures and the loop-erased random walk." This is not intended to be a comprehensive view but rather a personal selection of some key ideas…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.
These notes are based on a series of five lectures given during the summer school ``Interactions between Homotopy Theory and Algebra'' held at the University of Chicago in 2004.
This note is my comment on Glenn Shafer's discussion paper "Testing by betting", together with two online appendices comparing p-values and betting scores.
Rejoinder to "The Future of Indirect Evidence" [arXiv:1012.1161]
This paper is inspired by a seqfan post by Jeremy Gardiner. The post listed nine sequences with similar parities. In this paper I prove that the similarities are not a coincidence but a mathematical fact.
In this editorial, the organizers summarize facts and background about the event.
We revisit the problem of computing the spreading and covering numbers. We show a connection between some of the spreading numbers and the number of non-negative integer 2x2 matrices whose entries sum to d, and we construct an algorithm to…
This is a survey of some of Erd\H os's work on bases in additive number theory.