Category Archives: Convex polytopes

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

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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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A Mysterious Duality Relation for 4-dimensional Polytopes.

Two dimensions Before we talk about 4 dimensions let us recall some basic facts about 2 dimensions: A planar polygon has the same number of vertices and edges. This fact, which just asserts that the Euler characteristic of is zero, … Continue reading

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My Copy of Branko Grünbaum’s Convex Polytopes

Branko Grünbaum is my academic grandfather (see this highly entertaining post for a picture representing five academic generations). Gunter Ziegler just wrote a beautiful article in the Notices of the AMS on Branko Grunbaum’s  classic book “Convex Polytopes”, so this … Continue reading

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Eran Nevo: g-conjecture part 4, Generalizations and Special Cases

This is the fourth in a series of posts by Eran Nevo on the g-conjecture. Eran’s first post was devoted to the combinatorics of the g-conjecture and was followed by a further post by me on the origin of the g-conjecture. Eran’s second post was about … Continue reading

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