Mathematical Olympiads 2021: Problems from Around the World

Trong bài này tôi sẽ giới thiệu một số đề thi Olympic Toán năm 2021. Các đề thi được đăng ở dạng một file pdf không link, không ad và không watermark.

Update 17/7/2021.

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Gil Kalai

Some Problems March 28, 2023

In the previous post, Two Three Four posts ago I wrote about three recent breakthroughs in combinatorics and here I want to mention some problems that I posed over the years that are loosely related to these advances. Rank of … Continue reading →

Gil Kalai

Critical Times in Israel: Last Night’s Demonstrations March 27, 2023

Last night, the demonstrations in Israel regarding the “judicial reforms” escalated after the prime minister Netanyahu fired the defense minister Galant who called to stop the legislation. My wife and I enjoyed a concert and after it we heard loud … Continue reading →

Gil Kalai

An Aperiodic Monotile March 25, 2023

I suppose that most of you already heard about the first ever aperiodic planar tiling with one type of tiles. It was discovered by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. Amazing!!! Here are blogposts … Continue reading →

Gil Kalai

Some News from a Seminar in Cambridge March 16, 2023

On an old problems of Erdős (h/t Michael Simkin and Nati Linial) Here is a somewhat mysterious announcement for a combinatorics seminar lecture at Cambridge. Which old problems of Erdős are we talking about? Here is a picture from the … Continue reading →

Gil Kalai

Subspace Designs, Unit and Distinct Distances, and Piercing Standard Boxes. March 10, 2023

A lot of things are happening and let me briefly report on three major advancements in combinatorics. Peter Keevash, Ashwin Sah and Mehtaab Sawhney proved the existence of subspace designs with any given parameters, provided that the dimension of the … Continue reading →

Gil Kalai

Greg Kuperberg @ Tel Aviv University March 7, 2023

Greg Kuperberg is on a short visit in Israel and yesterday he gave a fantastic lecture on an improved bound for the Solovay-Kitaev theorem. Here is a videotaped lecture of Greg on the same topic in QIP2023. The Solovay-Kitaev theorem … Continue reading →

Gil Kalai

Israel AGT Day, Reichman University, March 5, 2023 March 4, 2023

We are running tomorrow the annual Israeli workshop in algorithmic game theory. Where: Reichman University. The conference will take place in room EL03, Adelson building. Program: here. Registration: here (free). Main speakers: Moshe Babaioff (Microsoft Research), Gil Kalai (Reichman University … Continue reading →

Gil Kalai

Alef’s Corner: Democracy (Israel, 2023) February 28, 2023

Democracy in Hebrew is דמוקרטיה represented by the letter “dalet” ד

Gil Kalai

Absolutely Sensational Morning News – Zander Kelley and Raghu Meka proved Behrend-type bounds for 3APs February 14, 2023

What is the density of a subset of that guarantees that contains a 3-term arithmetic progression? And, more generally, if the density of is what is the minimum number of 3-terms AP that contains? These problems and the more general … Continue reading →

Gil Kalai

The Trifference Problem January 23, 2023

Originally posted on Anurag's Math Blog: What is the largest possible size of a set of ternary strings of length , with the property that for any three distinct strings in , there is a position where they all…

Gil Kalai

Terence Tao

A Host–Kra F^omega_2-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the U^6(F^n_2) norm; The structure of totally disconnected Host–Kra–Ziegler factors, and the inverse theorem for the U^k Gowers uniformity norms on finite abelian groups of bounded torsion March 10, 2023

Asgar Jamneshan, Or Shalom, and myself have just uploaded to the arXiv our preprints “A Host–Kra -system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the norm” and “The structure of totally disconnected Host–Kra–Ziegler factors, and the inverse theorem for the Gowers uniformity norms on finite […]

Terence Tao

Mathematics for Humanity initiative – application deadline extended to June 1 March 9, 2023

The International Center for Mathematical Sciences in Edinburgh recently launched its “Mathematics for Humanity” initiative with a call for research activity proposals (ranging from small collaborations to courses, workshops and conferences) aimed at using mathematics to contributing to the betterment of humanity. (I have agreed to serve on the scientific co […]

Terence Tao

Would it be possible to create a tool to automatically diagram papers? February 18, 2023

This is a somewhat experimental and speculative post. This week I was at the IPAM workshop on machine assisted proof that I was one of the organizers of. We had an interesting and diverse range of talks, both from computer scientists presenting the latest available tools to formally verify proofs or to automate various aspects […]

Terence Tao

Infinite partial sumsets in the primes January 26, 2023

Tamar Ziegler and I have just uploaded to the arXiv our paper “Infinite partial sumsets in the primes“. This is a short paper inspired by a recent result of Kra, Moreira, Richter, and Robertson (discussed for instance in this Quanta article from last December) showing that for any set of natural numbers of positive upper […]

Terence Tao

Illustrating the Impact of the Mathematical Sciences January 12, 2023

Over the last few years, I have served on a committee of the National Academy of Sciences to produce some posters and other related media to showcase twenty-first century and its applications in the real world, suitable for display in classrooms or math departments. Our posters (together with some associated commentary, webinars on related topics, […]

Terence Tao

Special relativity and Middle-Earth December 19, 2022

This post is an unofficial sequel to one of my first blog posts from 2007, which was entitled “Quantum mechanics and Tomb Raider“. One of the oldest and most famous allegories is Plato’s allegory of the cave. This allegory centers around a group of people chained to a wall in a cave that cannot see […]

Terence Tao

An improvement to Bennett’s inequality for the Poisson distribution December 13, 2022

If , a Poisson random variable with mean is a random variable taking values in the natural numbers with probability distribution One is often interested in bounding upper tail probabilities for , or lower tail probabilities for . A standard tool for this is Bennett’s inequality: Proposition 1 (Bennett’s inequality) One has for and for […]

Terence Tao

Postdoctoral Research Positions in Mathematics and AI at the Sydney Mathematics Research Institute December 5, 2022

[The following information was provided to me by Geordie Williamson, who is Director of the Sydney Mathematics Research Institute – T.] We are currently advertising two positions in math and AI: Both positions are for three years and are based at the Sydney Mathematical Research Institute. The positions are research only, but teaching at the […]

Terence Tao

A counterexample to the periodic tiling conjecture November 30, 2022

Rachel Greenfeld and I have just uploaded to the arXiv our paper “A counterexample to the periodic tiling conjecture“. This is the full version of the result I announced on this blog a few months ago, in which we disprove the periodic tiling conjecture of Grünbaum-Shephard and Lagarias-Wang. The paper took a little longer than […]

Terence Tao

Trying out Mathstodon November 21, 2022

It’s been a while since I’ve actively participated in social media outside of this blog – I was active in Google Buzz/Google+ for a while, until that service closed – but I’ve decided to try out Mathstodon, one of the servers of the open source social media software platform Mastodon. As I understand it, Mastodon […]

Terence Tao

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