Category Archives: Convex polytopes

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

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 →

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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

Giving a talk at Eli and Ricky’s geometry seminar. (October 19, 2021)

Posted on October 17, 2021 by Gil Kalai

One of my favorite seminars in the world is the Courant Institute (NYU) Geometry seminar that Eli Goodman and Ricky Pollack started in the 1980s (I think). On Tuesday October 19, I will give a seminar, details follow. Jacob Eli … Continue reading →

Posted in Combinatorics, Convex polytopes, Geometry | Tagged | 1 Comment

To cheer you up in difficult times 26: Two real-life lectures yesterday at the Technion

Posted on June 9, 2021 by Gil Kalai

After 16 months without lecturing to an audience in my same location, I gave yesterday two lectures at the Technion in front of a live audience (and some additional audience in remote locations). The main lecture was in COMSOC 2021, … Continue reading →

Posted in Combinatorics, Convex polytopes, Economics, Games, Rationality | 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 | Leave a comment

Tomorrow: Boolean functions day at the TAU theory fest

Posted on January 2, 2020 by Gil Kalai

As part of the 2019/2020 TAU theory fest, tomorrow, Friday, January 3, 2020,  is a Boolean function day at Tel Aviv University. The five speakers are Esty Kelman, Noam Lifschitz, Renan Gross, Ohad Klein, and Naomi Kirshner. For more (and … Continue reading →

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Danny Nguyen and Igor Pak: Presburger Arithmetic Problem Solved!

Posted on March 22, 2019 by Gil Kalai

Short Presburger arithmetic is hard! This is a belated report on a remarkable breakthrough from 2017. The paper is Short Presburger arithmetic is hard, by Nguyen and Pak. Danny Nguyen Integer programming in bounded dimension: Lenstra’s Theorem Algorithmic tasks are … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Convex polytopes | Tagged , , , , , , , , | 2 Comments

Karim Adiprasito: The g-Conjecture for Vertex Decomposible Spheres

Posted on February 23, 2019 by Gil Kalai

J Scott Provan (site) The following post was kindly contributed by Karim Adiprasito. (Here is the link to Karim’s paper.) Update: See Karim’s comment on the needed ideas for extend the proof to the general case. See also  in the … Continue reading →

Posted in Combinatorics, Convex polytopes, Geometry, Guest blogger | Tagged , , , , | 9 Comments

Beyond the g-conjecture – algebraic combinatorics of cellular spaces I

Posted on June 20, 2018 by Gil Kalai

The g-conjecture for spheres is surely the one single conjecture I worked on more than on any other, and also here on the blog we had a sequence of posts about it by Eran Nevo (I,II,III,IV). Here is a great … Continue reading →

Posted in Combinatorics, Convex polytopes, Geometry | Tagged , , , , , , , , , , , , , , , , , , | 13 Comments