Category Archives: Geometry

Alef’s corner: Bicycles and the Art of Planar Random Maps

The artist behind Alef’s corner has a few mathematical designs and here are two new ones. (See Alef’s  website offering over 100 T-shirt designs.)   which was used for the official T-shirt for Jean-François Le Gall’s birthday conference. See also … Continue reading

Posted in Art, Combinatorics, Geometry, Probability | Tagged | Leave a comment

Mohammad Ghomi and Joel Spruck settled the Cartan-Hadamard conjecture!

Greetings from Oberwolfach from a great conference on algebraic, geometric, and topological combinatorics. Stay tuned for more pictures and updates from Oberwolfach and CERN, and also in case you did not see it already here is the link to the … Continue reading

Posted in Geometry, Uncategorized | Tagged , , | 5 Comments

Imre Bárány: Limit shape

Limit shapes are fascinating objects in the interface between probability and geometry and between the discrete and the continuous. This post is kindly contributed by Imre Bárány. What is a limit shape? There are finitely many convex lattice polygons contained … Continue reading

Posted in Combinatorics, Convexity, Geometry, Guest blogger, Probability | Tagged , | 4 Comments

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

Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska: Universal optimality of the E8 and Leech lattices and interpolation formulas

Henry Cohn A follow up paper on the tight bounds for sphere packings in eight and 24 dimensions. (Thanks, again, Steve, for letting me know.) For the 2016 breakthroughs see this post, this post of John Baez, this article by Erica Klarreich on … Continue reading

Posted in Algebra, Combinatorics, Geometry, Number theory | Tagged , , , , , , , | 1 Comment

Exciting Beginning-of-the-Year Activities and Seminars.

Let me mention two talks with very promising news by friends of the blog, Karim Adiprasito and Noam Lifshitz. As always, with the beginning of the academic year there are a lot of exciting activities,  things are rather hectic around,  … Continue reading

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ICM 2018 Rio (3) – Coifman, Goldstein, Kronheimer and Mrowka, and the Four Color Theorem

This post is my third report from ICM 2018. You may remember that I had planned to live-blog on the last four days of the congress but on Monday evening I realized that this was an unrealistic task and decided … Continue reading

Posted in Combinatorics, Geometry, ICM2018 | Tagged , , , | 2 Comments

Ricky and Branko

Two dear friends, and great geometers, Ricky Pollack and Branko Grünbaum  passed away a few weeks ago. Ricky was a close friend that both Mazi my wife and I loved, and we were both fascinated by his wisdom, charm and … Continue reading

Posted in Combinatorics, Convexity, Geometry, Obituary | Tagged , | 3 Comments

An Improved Bound for Weak Epsilon-Nets in the Plane, by Nathan Rubin, is on the arXive

The paper An Improved Bound for Weak Epsilon-Nets in the Plane, by Nathan Rubin is now on the arxive. we mentioned  the result in this post, and the problem in this post (my very first) over Tao’s blog What’s New. … Continue reading

Posted in Combinatorics, Geometry | Tagged , | Leave a comment

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 , , , , , , , , , , , , , , , , , , | 10 Comments