Category Archives: Algebra

Greg Kuperberg @ Tel Aviv University

Posted on March 7, 2023 by Gil Kalai

Greg Kuperberg is on a short visit in Israel and yesterday he gave a fantastic lecture on an improved bound for the Solovay-Kitaev theorem. Here is a videotaped lecture of Greg on the same topic in QIP2023. The Solovay-Kitaev theorem … Continue reading →

Posted in Algebra, Combinatorics, Computer Science and Optimization, Quantum | Tagged | Leave a comment

ICM 2022: Langlands Day

Posted on July 13, 2022 by Gil Kalai

ICM 2022 is running virtually and you can already watch all the videos of past lectures at the IMU You-Tube channel, and probably even if you are not among the 7,000 registered participants you can see them “live” on You-Tube … Continue reading →

Posted in Algebra, ICM2022, Number theory | Tagged , , , | Leave a comment

ICM 2022 awarding ceremonies (1)

Posted on July 6, 2022 by Gil Kalai

Hugo Duminil-Copin, June Huh, James Maynard and Maryna Viazovska were awarded the Fields Medal 2022 and Mark Braverman was awarded the Abacus Medal 2022. I am writing from Helsinki where I attended the meeting of the General Assembly of the … Continue reading →

Posted in Academics, Algebra, Applied mathematics, Combinatorics, Computer Science and Optimization, Convexity, Geometry, ICM2022, Probability | 7 Comments

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 , | 2 Comments

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

To cheer you up in difficult times 27: A major recent “Lean” proof verification

Posted on June 30, 2021 by Gil Kalai

“Lean is a functional programming language that makes it easy to write correct and maintainable code. You can also use Lean as an interactive theorem prover.” (See Lean’s homepage and see here for an introduction to lean.) Kevin Buzzard’s blog … Continue reading →

Posted in Algebra, Updates, What is Mathematics | Tagged , , | 5 Comments

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 | 3 Comments

To cheer you up in difficult times 21: Giles Gardam lecture and new result on Kaplansky’s conjectures

Posted on February 25, 2021 by Gil Kalai

There is a very famous conjecture of Irving Kaplansky that asserts that the group ring of a torsion free group does not have zero-divisors. Given a group G and a ring R, the group ring R[G] consists of formal (finite) … Continue reading →

Posted in Algebra | Tagged , | 8 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 , , , , | 7 Comments