Category Archives: Geometry

ICM 2018 Rio (5) Assaf Naor, Geordie Williamson and Christian Lubich

Posted on January 3, 2022 by Gil Kalai

This is my fifth and last report from ICM 2018 at Rio. I will talk a little about the three Wednesday plenary talks by Assaf Naor, Geordie Williamson, and Christian Lubich. See here for other posts about ICM2018. (For the … Continue reading →

Posted in Algebra, Analysis, Geometry, ICM2018 | Tagged , , | 3 Comments

Test your intuition 47: AGC-GTC-TGC-GTC-TGC-GAC-GATC-? what comes next in the sequence?

Posted on December 24, 2021 by Gil Kalai

Before getting to the main topic of this post, first, Happy New Year 2022 and Merry Christmas to all readers, and second, a quick update: A community blog to discuss open problems in algebraic combinatorics was created. Everybody is invited … Continue reading →

Posted in Algebra, Combinatorics, Geometry, Test your intuition | Tagged , | 1 Comment

To cheer you up in difficult times 34: Ringel Circle Problem solved by James Davies, Chaya Keller, Linda Kleist, Shakhar Smorodinsky, and Bartosz Walczak

Posted on December 11, 2021 by Gil Kalai

Gerhard Ringel considered in 1959 the following: Consider a finite family of circles such that every point in the plane is included in at most two circles. What is the minimum number of colors needed to color the circles so … Continue reading →

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

To cheer you up in difficult times 33: Deep learning leads to progress in knot theory and on the conjecture that Kazhdan-Lusztig polynomials are combinatorial.

Posted on December 4, 2021 by Gil Kalai

One of the exciting directions regarding applications of computers in mathematics is to use them to experimentally form new conjectures. Google’s DeepMind launched an endeavor for using machine learning (and deep learning in particular) for finding conjectures based on data. Two … Continue reading →

Posted in Algebra, Combinatorics, Geometry, What is Mathematics | 8 Comments

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 | 1 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