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.

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

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

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

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

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

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

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

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

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

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

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Tomorrow: Boolean functions day at the TAU theory fest

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!

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

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Karim Adiprasito: The g-Conjecture for Vertex Decomposible Spheres

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

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

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