Category Archives: Geometry

Subspace Designs, Unit and Distinct Distances, and Piercing Standard Boxes.

Posted on March 10, 2023 by Gil Kalai

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 →

Posted in Combinatorics, Geometry | Tagged , , , , , , | 2 Comments

James Davies: Every finite colouring of the plane contains a monochromatic pair of points at an odd distance from each other.

Posted on October 19, 2022 by Gil Kalai

Here is a lovely piece of news: the following paper by James Davies was posted on the arXive a few weeks ago. The paper uses spectral methods to settle an old question, posed in 1994, by Moshe Rosenfeld. (See this … Continue reading →

Posted in Combinatorics, Geometry | Tagged , | 1 Comment

Bo’az Klartag and Joseph Lehec: The Slice Conjecture Up to Polylogarithmic Factor!

Posted on October 15, 2022 by Gil Kalai

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 pleasure to report on a further fantastic progress on these … Continue reading →

Posted in Analysis, Computer Science and Optimization, Convexity, Geometry, Probability | Tagged , | 3 Comments

Test Your intuition 51

Posted on October 11, 2022 by Gil Kalai

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 average volume of a … Continue reading →

Posted in Convexity, Geometry, Probability, Test your intuition | Tagged | 12 Comments

Alexander A. Gaifullin: Many 27-vertex Triangulations of Manifolds Like the Octonionic Projective Plane (Not Even One Was Known Before).

Posted on August 19, 2022 by Gil Kalai

  From top left clockwise: Alexander Gaifullin, Denis Gorodkov, Ulrich Brehm, Wolfgang Kühnel  Here is the paper: Alexander A. Gaifullin: 634 vertex-transitive and more than 10¹⁰³ non-vertex-transitive 27-vertex triangulations of manifolds like the octonionic projective plane  Abstract with annotation: In … Continue reading →

Posted in Combinatorics, Geometry | Tagged , , , | 2 Comments

ICM 2022 awarding ceremonies (1)

Posted on July 6, 2022 by Gil Kalai

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 →

Posted in Academics, Algebra, Applied mathematics, Combinatorics, Computer Science and Optimization, Convexity, Geometry, ICM2022, Probability | 7 Comments

Past and Future Events

Posted on May 9, 2022 by Gil Kalai

Quick announcements of past (recorded) and future events 1) Shachar Lovett was the Erdos Speaker for 2022 and his great talks are recorded. (Lecture 1, Tensor ranks and their applications lecture 2, The monomial structure of Boolean functions, lecture 3, … Continue reading →

Posted in Combinatorics, Conferences, Convexity, Geometry, Quantum | Leave a comment

Combinatorial Convexity: A Wonderful New Book by Imre Bárány

Posted on March 21, 2022 by Gil Kalai

A few days ago I received by mail Imre Bárány’s new book Combinatorial Convexity. The book presents Helly-type theorems and other results in convexity with combinatorial flavour. The choice of material and the choice of proofs is terrific and it … Continue reading →

Posted in Combinatorics, Convexity, Geometry | Tagged | Leave a comment

Ehud Friedgut: How many cubes of 2×2×2 fit into a box of size 8×4×3? (TYI 49)

Posted on February 16, 2022 by Gil Kalai

This blog post is kindly written by Ehud Friedgut. My daughter, Shiri, who’s in seventh grade, had the following question in a math exam: How many cubes of 2×2×2 fit into a box of size 8×4×3? Shiri divided the volumes, … Continue reading →

Posted in Geometry, Riddles, Test your intuition | Tagged , , , | 6 Comments

ICM 2018 Rio (5) Assaf Naor, Geordie Williamson and Christian Lubich

Posted on January 3, 2022 by Gil Kalai

This is my fifth and last report from ICM 2018 at Rio. I will talk a little about the three Wednesday plenary talks by Assaf Naor, Geordie Williamson, and Christian Lubich. See here for other posts about ICM2018. (For the … Continue reading →

Posted in Algebra, Analysis, Geometry, ICM2018 | Tagged , , , | 3 Comments