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Category Archives: Convex polytopes
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
Posted in Convex polytopes, Convexity, Updates
Tagged Deane Yang, Erwin Lutwak, Gaoyong Zhang, Károly Böröczky
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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
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
Posted in Combinatorics, Convex polytopes, Economics, Games, Rationality
Tagged COMSOC 2021
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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
Posted in Combinatorics, Convex polytopes, Convexity, Geometry
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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
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 g-conjecture, J Scott Provan, Karim Adiprasito, Leonid Gurvits, Lou Billera
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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
Posted in Combinatorics, Convex polytopes, Geometry
Tagged Anders Bjorner, Bob MacPherson, Carl Lee, Ed Swartz, Eran Nevo, g-conjecture, Günter Ziegler, Isabella Novik, June Huh, Kalle Karu, Karim Adiprasito, Kazhdan-Lustig polynomials, Lou Billera, Marge Bayer, Peter McMullen, Richard Stanley, Ron Adin, Satoshi Murai, Tom Braden
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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
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
Posted in Combinatorics, Convex polytopes, People
Tagged Branko Grunbaum, Dom de Caen, Günter Ziegler
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Combinatorics and more 