Number Theory – Page 2

Một số trang về Olympic Toán

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To cheer you up in difficult times 36: The Immense Joy of Fake Reverse Parking August 11, 2022
Fake reverse parking When I was young my mother Carmela Kalai told me: “Always remember, Gili, how wonderful movies are and how happy I was to be born in the era of movies.” My father Hanoch Kalai told me: “Everything … Continue reading →
Gil Kalai
Ordinary computers can beat Google’s quantum computer after all August 6, 2022
Science magazine has an article written by Adrian Cho Ordinary computers can beat Google’s quantum computer after all. It is about the remarkable progress in classical simulations of sampling task like those sampling tasks that led to the 2019 Google’s … Continue reading →
Gil Kalai
Test Your Intuition 50. Two-Player Random Walk; Can You Detect Who Did Not Follow the Rules? August 3, 2022
Ruth and Ron start together at the origin and take a walk on the integers. Every day they make a move. They take turns in flipping a coin and they move together right or left according to the outcome. Their … Continue reading →
Gil Kalai
ICM 2022. Kevin Buzzard: The Rise of Formalism in Mathematics July 17, 2022
In this post I would like to report on Kevin Buzzard’s spectacular lecture on moving mathematics toward formal mathematical proofs. (Here are the slides.) The picture above is based on images from the other spectacular Saturday morning lecture by Laure … Continue reading →
Gil Kalai
ICM 2022: Langlands Day July 13, 2022
ICM 2022 is running virtually and you can already watch all the videos of past lectures at the IMU You-Tube channel, and probably even if you are not among the 7,000 registered participants you can see them “live” on You-Tube … Continue reading →
Gil Kalai
ICM 2022 awarding ceremonies (1) July 6, 2022
Hugo Duminil-Copin, June Huh, James Maynard and Maryna Viazovska were awarded the Fields Medal 2022 and Mark Braverman was awarded the Abacus Medal 2022. I am writing from Helsinki where I attended the meeting of the General Assembly of the … Continue reading →
Gil Kalai
ICM 2022 Virtual Program, Live events, and Dynamics Week in Jerusalem June 30, 2022
ICM 2022 Next Tuesday, July 5 2022 will be the opening day of the International Congress of Mathematicians (ICM 2022) that, because of the war in Ukraine, will be fully virtual. Here is the link for the program for ICM … Continue reading →
Gil Kalai
Algorithmic Game Theory: Past, Present, and Future June 26, 2022
Noam Nisan is 60 Today, June 26 2022, is the opening day of Algorithmic Game Theory: Past, Present, and Future, a workshop in honor of Noam Nisan’s 60th Birthday. The workshop takes place on June 26-30 2022, at the CS … Continue reading →
Gil Kalai
Richard Stanley: Enumerative and Algebraic Combinatorics in the1960’s and 1970’s June 17, 2022
In his comment to the previous post by Igor Pak, Joe Malkevitch referred us to a wonderful paper by Richard Stanley on enumerative and algebraic combinatorics in the 1960’s and 1970’s. See also this post on Richard’s memories regarding the … Continue reading →
Gil Kalai
Igor Pak: How I chose Enumerative Combinatorics June 16, 2022
Originally posted on Igor Pak's blog: Apologies for not writing anything for awhile. After Feb 24, the math part of the “life and math” slogan lost a bit of relevance, while the actual events were stupefying to the point…
Gil Kalai

Using the Smith normal form to manipulate lattice subgroups and closed torus subgroups July 20, 2022
Let denote the space of matrices with integer entries, and let be the group of invertible matrices with integer entries. The Smith normal form takes an arbitrary matrix and factorises it as , where , , and is a rectangular diagonal matrix, by which we mean that the principal minor is diagonal, with all other […]
Terence Tao
Request for comments from the ICM Structure Committee July 17, 2022
[This post is collectively authored by the ICM structure committee, whom I am currently chairing – T.] The ICM structure committee is responsible for the preparation of the Scientific Program of the International Congress of Mathematicians (ICM). It decides the structure of the Scientific Program, in particular, the number of plenary lectures, the sections a […]
Terence Tao
ICM and IMU award ceremony begins tomorrow July 4, 2022
I’m currently in Helsinki, Finland for the General Assembly meeting of the International Mathematical Union (IMU), which runs the International Congress of Mathematicians (ICM) as well as several other events and initiatives. In particular the assembly voted on the location of the 2026 ICM; it will be held in Philadelphia, USA (with the general assembly […] […]
Terence Tao
Registration for the virtual ICM is now open June 2, 2022
The (now virtual) 2022 International Congress of Mathematicians, which will be held on July 6-14, now has open registration (free of charge). I’ll also take this opportunity to mention that there are a large number of supporting satellite events for the virtual ICM, which are listed on this web page. I’d like to draw particular […]
Terence Tao
Notes on inverse theorem entropy May 27, 2022
Let be a finite set of order ; in applications will be typically something like a finite abelian group, such as the cyclic group . Let us define a -bounded function to be a function such that for all . There are many seminorms of interest that one places on functions that are bounded by […]
Terence Tao
Partially specified mathematical objects, ambient parameters, and asymptotic notation May 11, 2022
In orthodox first-order logic, variables and expressions are only allowed to take one value at a time; a variable , for instance, is not allowed to equal and simultaneously. We will call such variables completely specified. If one really wants to deal with multiple values of objects simultaneously, one is encouraged to use the language […]
Terence Tao
Higher uniformity of arithmetic functions in short intervals I. All intervals April 11, 2022
Kaisa Matomäki, Xuancheng Shao, Joni Teräväinen, and myself have just uploaded to the arXiv our preprint “Higher uniformity of arithmetic functions in short intervals I. All intervals“. This paper investigates the higher order (Gowers) uniformity of standard arithmetic functions in analytic number theory (and specifically, the Möbius function , the von Mango […]
Terence Tao
Nominations for 2023 Doob prize now open April 7, 2022
Just a brief announcement that the AMS is now accepting (until June 30) nominations for the 2023 Joseph L. Doob Prize, which recognizes a single, relatively recent, outstanding research book that makes a seminal contribution to the research literature, reflects the highest standards of research exposition, and promises to have a deep and long-term impact in […]
Terence Tao
Web page for the Short Communication Satellite (SCS) of the 2022 virtual ICM now live March 30, 2022
Just a brief update to the previous post. Gerhard Paseman and I have now set up a web site for the Short Communication Satellite (SCS) for the virtual International Congress of Mathematicians (ICM), which will be an experimental independent online satellite event in which short communications on topics relevant to one or two of the […]
Terence Tao
Short communication satellite event for the 2022 virtual ICM? March 20, 2022
[As with previous posts regarding ICM satellite events, I am authoring this post as an individual, and not in my capacity as chair of the ICM Structure Committee, which does not have any advisory or supervisory role over ICM satellite events – T.] One of the traditional features of the International Congress of Mathematicians are […]
Terence Tao

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