Category Archives: Geometry

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

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 , | Leave a comment

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

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 , | 2 Comments

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 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).

  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 , , , | 1 Comment

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 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 | 5 Comments

Past and Future Events

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

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

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

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

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

Test your intuition 47: AGC-GTC-TGC-GTC-TGC-GAC-GATC-? what comes next in the sequence?

Before getting to the main topic of this post, first, Happy New Year 2022 and Merry Christmas to all readers, and second, a quick update: A community blog to discuss open problems in algebraic combinatorics was created. Everybody is invited … Continue reading

Posted in Algebra, Combinatorics, Geometry, Test your intuition | Tagged , | 1 Comment