Category Archives: Geometry

November’s Lectures, 2025

Posted on December 21, 2025 by Gil Kalai

Happy Chanukah, everybody! There is a lot of academic activity around, and the ceasefire in Gaza has brought some relief and hope. Let me tell you about the (unusually high number of) lectures I attended in November 2025, in reverse … Continue reading →

Posted in AI, Combinatorics, Computer Science and Optimization, Geometry, Physics, Quantum, Updates | 11 Comments

Kazhdan Seminar fall 2025 – Starting Today Oct. 19, 2026.

Posted on October 19, 2025 by Gil Kalai

This semester as a part of Kazhdan Sunday seminars we will have the following two activities (see description below) 12-14 Nati Linial and Yuval Peled,  “Recent advances in combinatorics” 14-16 Jake Solomon “Curve counts and quadratic forms”.  Both seminars will take … Continue reading →

Posted in Combinatorics, Geometry, Updates | Tagged , , , | 1 Comment

Dror Bar-Natan and Roland Van der Veen – A Fast, Strong, and Fun knot invariant!

Posted on September 25, 2025 by Gil Kalai

Dror Bar-Natan (homepage, Wikipedia) told me about his work with Roland Van der Veen (homepage, arXiv, YouTube) on a wonderful knot invariant which distinguishes knots much better than other knot invariants, and can be computed quickly even for knots of … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Geometry | Tagged , , | 1 Comment

Amazing: Jie Ma, Wujie Shen, and Shengjie Xie Gave an Exponential Improvement for Ramsey Lower Bounds

Posted on July 23, 2025 by Gil Kalai

h/t Benny Sudakov The Ramsey number R(ℓ,k) is the smallest integer n such that in any two-coloring of the edges of the complete graph on n vertices, , by red and blue, there is either a red (a complete graph … Continue reading →

Posted in Combinatorics, Geometry, Probability, Updates | Tagged , , | 6 Comments

Sergey Avvakumov and Alfredo Hubard Construct Cubical Spheres with Many Facets!

Posted on June 24, 2025 by Gil Kalai

In this post, I discuss a remarkable new paper Cubulating the sphere with many facets by Sergey Avvakumov and Alfredo Hubard Abstract: For each we construct cube complexes homeomorphic to the -sphere with vertices in which the number of facets … Continue reading →

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

Shakhar Smorodinsky’s Solution to a Radon-Type Problem

Posted on June 18, 2025 by Gil Kalai

A brief update: Since Friday June 13 Israel has been engaged in a direct war with Iran. This follows two major missiles attacks of Iran against Israel in April and October 2024, as well as Iran’s central role in the … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Geometry, Updates | Tagged , , , , | 3 Comments

Ethereum Foundation Talk and Conversation: A Critical View on Quantum Computing & A geometry day honoring Micha Sharir

Posted on June 3, 2025 by Gil Kalai

Ethereum Foundation talk, today This afternoon (Tuesday, June 3, 2025) at 17:00 Israel time I give a zoom lecture on A Critical View on Quantum Computing. The lecture is hosted by the Ethereum Foundation and the 90 minute events will … Continue reading →

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Cosmin Pohoata and Daniel G. Zhu: Hypergraphic Zonotopes and Acyclohedra

Posted on May 30, 2025 by Gil Kalai

I would like to draw your attention to the short beautiful paper Hypergraphic Zonotopes and Acyclohedra by Cosmin Pohoata and Daniel G. Zhu. The paper introduces higher-uniformity analogue of graphic zonotopes and permutohedra, and provides formulas for their volume, and, … Continue reading →

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Bo’az Klartag: Striking new Lower Bounds for Sphere Packing in High Dimensions

Posted on April 9, 2025 by Gil Kalai

Two day ago, a new striking paper appeared on the arXiv Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid, by Bo’az Klartag. Abstract: We prove that in any dimension $latex n$ there exists an origin-symmetric ellipsoid … Continue reading →

Posted in Combinatorics, Convexity, Geometry, Updates | Tagged , , | 2 Comments

Hong Wang and Joshua Zahl’s Solution for the Kakeya Problem in Three Dimensions – Reflections and Links

Posted on April 4, 2025 by Gil Kalai

As many of you likely heard by now, Hong Wang and Joshua Zahl proved the The Kakeya Conjecture in three dimensions. Hong Wang and Joshua Zahl, Volume estimates for unions of convex sets, and the Kakeya set conjecture in three … Continue reading →

Posted in Analysis, Geometry, Updates | Tagged , , | 3 Comments