Category Archives: Geometry

Giving a talk at Eli and Ricky’s geometry seminar. (October 19, 2021)

Posted on October 17, 2021 by Gil Kalai

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 →

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

Let me tell you about three of my recent papers

Posted on August 5, 2021 by Gil Kalai

  Let me tell you briefly about three of my papers that were recently accepted for publication. Relative Leray numbers via spectral sequences with Roy Meshulam, Helly-type problems with Imre Bárány, and Statistical aspects of quantum supremacy experiments with Yosi … Continue reading →

Posted in Combinatorics, Convexity, Geometry, Quantum, Statistics | Tagged , , , , | Leave a comment

To cheer you up in difficult times 25: some mathematical news! (Part 2)

Posted on May 20, 2021 by Gil Kalai

Topology Quasi-polynomial algorithms for telling if a knot is trivial Marc Lackenby announced a quasi-polynomial time algorithm to decide whether a given knot is the unknot! This is a big breakthrough. This question is known to be both in NP … Continue reading →

Posted in Algebra, Combinatorics, Geometry, Number theory | 2 Comments

Alef Corner: ICM2022

Posted on May 6, 2021 by Gil Kalai

Alef’s new piece for ICM 2022 will surely cheer you up!

Posted in Art, Combinatorics, Geometry, ICM2022 | Tagged , | Leave a comment

To cheer you up in difficult times 22: some mathematical news! (Part 1)

Posted on March 23, 2021 by Gil Kalai

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 | Leave a comment

Cheerful News in Difficult Times: The Abel Prize is Awarded to László Lovász and Avi Wigderson

Posted on March 17, 2021 by Gil Kalai

The Abel Prize was awarded earlier today to László Lovász and Avi Wigderson “for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics.” Congratulations to Laci … Continue reading →

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

Amazing: Simpler and more general proofs for the g-theorem by Stavros Argyrios Papadakis and Vasiliki Petrotou, and by Karim Adiprasito, Stavros Argyrios Papadakis, and Vasiliki Petrotou.

Posted on January 21, 2021 by Gil Kalai

Stavros Argyrios Papadakis, Vasiliki Petrotou, and Karim Adiprasito In 2018, I reported here about Karim Adiprasito’s proof of the g-conjecture for simplicial spheres.  This conjecture by McMullen from 1970 was considered a holy grail of algebraic combinatorics and it resisted … Continue reading →

Posted in Algebra, Combinatorics, Geometry | Tagged , , , , | 5 Comments

Igor Pak: What if they are all wrong?

Posted on January 19, 2021 by Gil Kalai

Originally posted on Igor Pak's blog:
Conjectures are a staple of mathematics. They are everywhere, permeating every area, subarea and subsubarea. They are diverse enough to avoid a single general adjective. They come in al shapes and sizes. Some…

Posted in Combinatorics, Computer Science and Optimization, Geometry, What is Mathematics | Tagged | 7 Comments

Open problem session of HUJI-COMBSEM: Problem #5, Gil Kalai – the 3ᵈ problem

Posted on January 10, 2021 by Gil Kalai

This post continues to describe problems presented at our open problems session back in November 2020. Here is the first post in the series.  Today’s problem was presented by me, and it was an old 1989 conjecture of mine. A … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Geometry, Open problems | 5 Comments

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

Posted on December 21, 2020 by Gil Kalai

This post gives some background to  a recent amazing breakthrough  paper: An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture by Yuansi Chen. Congratulations Yuansi! The news Yuansi Chen gave an almost constant bounds for Bourgain’s … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Convexity, Geometry | Tagged | 6 Comments