Category Archives: Convexity

Barnabás Janzer: Rotation inside convex Kakeya sets

Posted on November 16, 2022 by Gil Kalai

Barnabás Janzer studied the following question: Suppose we have convex body in that contains a copy of a convex body in every orientation. Is it always possible to move any one copy of to another copy of , keeping inside … Continue reading →

Posted in Convexity, Test your intuition | 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

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

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 , , , | 1 Comment

The Logarithmic Minkowski Problem

Posted on November 22, 2021 by Gil Kalai

The logarithmic origin of Manhattan We are spending the fall semester in NYC at NYU and yesterday* I went to lunch with two old friends Deane Yang and Gaoyong Zhang. They told me about the logarithmic Minkowski problem, presented in the … Continue reading →

Posted in Convex polytopes, Convexity, Updates | Tagged , , , | 2 Comments

Let me tell you about three of my recent papers

Posted on August 5, 2021 by Gil Kalai

  Let me tell you briefly about three of my papers that were recently accepted for publication. Relative Leray numbers via spectral sequences with Roy Meshulam, Helly-type problems with Imre Bárány, and Statistical aspects of quantum supremacy experiments with Yosi … Continue reading →

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

To cheer you up in difficult times 22: some mathematical news! (Part 1)

Posted on March 23, 2021 by Gil Kalai

To cheer you up, in these difficult times, here are (in two parts) some mathematical news that I heard in personal communications or on social media. (Maybe I will write later, in more details,  about few of them that are … Continue reading →

Posted in Combinatorics, Convex polytopes, Convexity, Geometry | 2 Comments