- Reflections: On the Occasion of Ron Adin’s and Yuval Roichman’s Birthdays, and FPSAC 2021
- ICM 2018 Rio (5) Assaf Naor, Geordie Williamson and Christian Lubich
- Test your intuition 47: AGC-GTC-TGC-GTC-TGC-GAC-GATC-? what comes next in the sequence?
- Cheerful news in difficult times: Richard Stanley wins the Steele Prize for lifetime achievement!
- Combinatorial Theory is Born
- To cheer you up in difficult times 34: Ringel Circle Problem solved by James Davies, Chaya Keller, Linda Kleist, Shakhar Smorodinsky, and Bartosz Walczak
- Good Codes papers are on the arXiv
- 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.
- The Logarithmic Minkowski Problem
Top Posts & Pages
- Navier-Stokes Fluid Computers
- The Intermediate Value Theorem Applied to Football
- TYI 30: Expected number of Dice throws
- Believing that the Earth is Round When it Matters
- To Cheer You Up in Difficult Times 31: Federico Ardila's Four Axioms for Cultivating Diversity
- Amazing: Karim Adiprasito proved the g-conjecture for spheres!
- 'Gina Says'
- To cheer you up in difficult times 27: A major recent "Lean" proof verification
- Happy Birthday Richard Stanley!
Category Archives: Algebra
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
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
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
“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
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
To cheer you up in difficult times 21: Giles Gardam lecture and new result on Kaplansky’s conjectures
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
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.
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
To cheer you up in difficult times 13: Triangulating real projective spaces with subexponentially many vertices
Wolfgang Kühnel Today I want to talk about a new result in a newly arXived paper: A subexponential size by Karim Adiprasito, Sergey Avvakumov, and Roman Karasev. Sergey Avvakumov gave about it a great zoom seminar talk about the result … Continue reading
To cheer you up in difficult times 7: Bloom and Sisask just broke the logarithm barrier for Roth’s theorem!
Thomas Bloom and Olof Sisask: Breaking the logarithmic barrier in Roth’s theorem on arithmetic progressions, arXiv:200703528 Once again Extraordinary news regarding Roth Theorem! (I thank Ryan Alweiss for telling me about it and Rahul Santhanam for telling me … Continue reading
A small update from Israel and memories from Singapore: Partha Dasgupta, Robin Mason, Frank Ramsey, and 007
A small update about the situation here in Israel Eight weeks ago I wrote that my heart goes out to the people of Wuhan and China, and these days my heart goes out to people in Italy, Spain, the US, … Continue reading