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Category Archives: Convex polytopes
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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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
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged Eran Nevo, g-conjecture
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Touching Simplices and Polytopes: Perles’ argument
Joseph Zaks (1984), picture taken by Ludwig Danzer (OberWolfach photo collection) The story I am going to tell here was told in several places, but it might be new to some readers and I will mention my own angle, … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry, Open problems
Tagged Joseph Zaks, Micha A. Perles
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