Recent Comments
-
Recent Posts
- To cheer you up in difficult times 21: Giles Gardam lecture and new result on Kaplansky’s conjectures
- Nostalgia corner: John Riordan’s referee report of my first paper
- At the Movies III: Picture a Scientist
- At the Movies II: Kobi Mizrahi’s short movie White Eye makes it to the Oscar’s short list.
- And the Oscar goes to: Meir Feder, Zvi Reznic, Guy Dorman, and Ron Yogev
- Thomas Vidick: What it is that we do
- To cheer you up in difficult times 20: Ben Green presents super-polynomial lower bounds for off-diagonal van der Waerden numbers W(3,k)
- To cheer you up in difficult times 19: Nati Linial and Adi Shraibman construct larger corner-free sets from better numbers-on-the-forehead protocols
- Possible future Polymath projects (2009, 2021)
Top Posts & Pages
- To Cheer You Up in Difficult Times 15: Yuansi Chen Achieved a Major Breakthrough on Bourgain's Slicing Problem and the Kannan, Lovász and Simonovits Conjecture
- To cheer you up in difficult times 21: Giles Gardam lecture and new result on Kaplansky's conjectures
- TYI 30: Expected number of Dice throws
- 8866128975287528³+(-8778405442862239)³+(-2736111468807040)³
- The Argument Against Quantum Computers - A Very Short Introduction
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Amazing: Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen proved that MIP* = RE and thus disproved Connes 1976 Embedding Conjecture, and provided a negative answer to Tsirelson's problem.
- Possible future Polymath projects (2009, 2021)
- Photonic Huge Quantum Advantage ???
RSS
Category Archives: Convex polytopes
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
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
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
11 Comments
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
4 Comments
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
2 Comments
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
Leave a comment
Convex Polytopes: Seperation, Expansion, Chordality, and Approximations of Smooth Bodies
I am happy to report on two beautiful results on convex polytopes. One disproves an old conjecture of mine and one proves an old conjecture of mine. Loiskekoski and Ziegler: Simple polytopes without small separators. Does Lipton-Tarjan’s theorem extends to high … Continue reading
The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond
A quick schematic road-map to these new geometric objects. The positroidron can be seen as a cellular structure on the nonnegative Grassmanian – the part of the real Grassmanian G(m,n) which corresponds to m by n matrices with all m by … Continue reading