Clik here to view.
Clik here to view.
Amazing: There is no Percolation at the Critical Probability in all...
The θ(p꜀) = 0 conjecture is solved in all dimensions. In 2024 Gady Kozma and Shahaf Nitzan showed how to derive the dying percolation conjecture from a proposed conjecture about percolation on general...
View ArticleClik here to view.
Test Your Intuition 59 : The Conclave Process
When the papacy becomes vacant, a new pope is elected through a procedure known as the conclave. Cardinal-electors from around the world gather in the Sistine Chapel and vote in successive rounds. In...
View ArticleClik here to view.
ICM 2026: A Magical Saturday Afternoon with Park, Braden and Proudfoot, and Meka
Saturday afternoon, July 25, was quite magical for me: all three beautiful talks were closely related to my interests and to my own work. Here is a brief personal description of the lectures, with...
View ArticleClik here to view.
Amazing: Jie Ma, Wujie Shen, and Shengjie Xie Gave an Exponential Improvement...
h/t Benny Sudakov The Ramsey number R(ℓ,k) is the smallest integer n such that in any two-coloring of the edges of the complete graph on n vertices, , by red and blue, there is either a red (a complete...
View ArticleClik here to view.
Recent Academic Events
With members of the discrete geometry seminar in Prague. The 2025 Colloquia in Combinatorics took place in QMUL and UCL, 7 and 8 May 2025. 2025 is the 18th year of the Colloquia in Combinatorics, and...
View ArticleClik here to view.
Annotated Pictures from Fall 2024
Apart from pictures, I write about the very first “Test your Intuition” question, a pioneering work of Tutubalin, the hierarchy of valuations of Lehman, Lehman, and Nisan, and three conjectures of Miki...
View ArticleClik here to view.
Jiaoyang Huang, Theo Mckenzie, Horng-Tzer Yau: Ramanujan Property and Edge...
A central problem in combinatorics, probability theory, and analysis is to understand the spectrum of random d-regular graphs G with vertices. The following paper marks a huge leap in our...
View ArticleClik here to view.
Timothy Chow’s Amazing Fifteen Boxes Puzzle (TYI 56)
TYI56 asked the following question of Timothy Chow: You have fifteen boxes labelled with the English letters from A to O. Two identical prizes are placed in two (distinct) boxes chosen at random....
View ArticleClik here to view.
Test Your Intuition 56: Fifteen Boxes Puzzle
Andrew and Barbara are playing a game. Fifteen boxes are arranged in a 3-by-5 grid, labeled with the letters A through O, as shown below. A B C D E F G H I J K L M N O The organizers of the game have...
View ArticleClik here to view.
Test Your Intuition 55: The Case of Two Screening Tests
Here is a great question invented by Michele Piccione and Ariel Rubinstein. (Let me use this opportunity to recommend their mind boggling 1997 paper on the absent-minded driver.) The question (TYI 55)...
View ArticleClik here to view.
TYI 54: A Variant of Elchanan Mossel’s Amazing Dice Paradox
The following question was inspired by recent comments to the post on Elchanan Mossel’s amazing Dice Paradox. A fair dice is a dice that when thrown you get each of the six possibilities with...
View ArticleClik here to view.
ChatGPT Meets Elchanan Mossel’s Dice Problem
One of the greatest hits of this blog was Elchanan Mossel’s dice problem, asked here and answered here. Here is how chatGPT (the free version) handles the problem. You throw a die until you get 6. What...
View ArticleClik here to view.
Bo’az Klartag and Joseph Lehec: The Slice Conjecture Up to Polylogarithmic...
Bo’az Klartag (right) and Joseph Lehec (left) In December 2020, we reported on Yuansi Chen breakthrough result on Bourgain’s alicing problem and the Kannan Lovasz Simonovits conjecture. It is a...
View ArticleClik here to view.
Test Your intuition 51
Suppose that and are two compact convex sets in space. Suppose that contains . Now consider two quantities is the average volume of a simplex forms by four points in drawn uniformly at random. is the...
View ArticleClik here to view.
Answer to Test Your Intuition 50: Detecting a Deviator
Two weeks ago we asked: 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...
View ArticleClik here to view.
Test Your Intuition 50. Two-Player Random Walk; Can You Detect Who Did Not...
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....
View ArticleClik here to view.
ICM 2022 awarding ceremonies (1)
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...
View ArticleClik here to view.
Amazing: Jinyoung Park and Huy Tuan Pham settled the expectation threshold...
A brief summary: In the paper, A proof of the Kahn-Kalai conjecture, Jinyoung Park and Huy Tuan Pham proved the 2006 expectation threshold conjecture posed by Jeff Kahn and me. The proof is wonderful....
View ArticleClik here to view.
Face to face talks and recorded videotaped introductions
Many face to face activities are now resuming. Last week I took part in a great conference on high dimensional expanders at the Simons Foundation, I recently gave real life talks with large audiences...
View Article
