Category Archives: Combinatorics

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 , , , | 1 Comment

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 | 5 Comments

Richard Stanley: Enumerative and Algebraic Combinatorics in the1960’s and 1970’s

Posted on June 17, 2022 by Gil Kalai

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 →

Posted in Combinatorics, What is Mathematics | Tagged | 1 Comment

Igor Pak: How I chose Enumerative Combinatorics

Posted on June 16, 2022 by Gil Kalai

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…

Posted in Combinatorics, What is Mathematics | Tagged | 1 Comment

Oliver Janzer and Benny Sudakov Settled the Erdős-Sauer Problem

Posted on May 20, 2022 by Gil Kalai

Norbert Sauer The news in brief:  In the new paper Resolution of the Erdős-Sauer problem on regular subgraphs Oliver Janzer and Benny Sudakov proved that any graph G with vertices and more than edges contains a k-regular subgraph. This bound … Continue reading →

Posted in Combinatorics | Tagged , | 6 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

Joshua Hinman proved Bárány’s conjecture on face numbers of polytopes, and Lei Xue proved a lower bound conjecture by Grünbaum.

Posted on April 29, 2022 by Gil Kalai

Joshua Hinman proved Bárány’s conjecture. One of my first posts on this blog was a 2008 post Five Open Problems Regarding Convex Polytopes, now 14 years later, I can tell you about the first problem on the list to get solved. … Continue reading →

Posted in Combinatorics, Convex polytopes | Tagged , , , | 4 Comments

Amazing: Jinyoung Park and Huy Tuan Pham settled the expectation threshold conjecture!

Posted on April 2, 2022 by Gil Kalai

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. Congratulations Jinyoung and Huy Tuan! Updates: … Continue reading →

Posted in Combinatorics, Probability | Tagged , | 7 Comments

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

Chaim Even-Zohar, Tsviqa Lakrec, and Ran Tessler present: The Amplituhedron BCFW Triangulation

Posted on March 5, 2022 by Gil Kalai

There is a recent breakthrough paper The Amplituhedron BCFW Triangulation by Chaim Even-Zohar, Tsviqa Lakrec, and Ran Tessler Abstract:  The amplituhedron   is a geometric object, introduced by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum … Continue reading →

Posted in Combinatorics, Convex polytopes, Convexity, Physics | Tagged , , , | Leave a comment