Category Archives: Algebra

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

“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 , , | 4 Comments

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

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

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

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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

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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

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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

Posted in Algebra, Combinatorics, Updates | Tagged , | 22 Comments

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

Posted in Algebra, Combinatorics, Conferences, Economics, Taxi-and-other-stories, Updates | Tagged , , , , , , , , | 3 Comments

Hoi Nguyen and Melanie Wood: Remarkable Formulas for the Probability that Projections of Lattices are Surjective

Following a lecture by Hoi Nguyen at Oberwolfach, I would like to tell you a little about the paper: Random integral matrices: universality of surjectivity and the cokernel by Hoi Nguyen and Melanie Wood. Two background questions: Hoi started with … Continue reading

Posted in Algebra, Combinatorics, Number theory, Probability | Tagged , | 6 Comments

Amazing: Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen proved that MIP* = RE and thus disproved Connes 1976 Embedding Conjecture, and provided a negative answer to Tsirelson’s problem.

A few days ago an historic 160-page paper with a very short title MIP*=RE was uploaded to the arXive by Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen.  I am thankful to Dorit Aharonov and Alon Rosen … Continue reading

Posted in Algebra, Analysis, Combinatorics, Computer Science and Optimization, Physics, Quantum | Tagged , , , , | 13 Comments

Do Not Miss: Abel in Jerusalem, Sunday, January 12, 2020

From left: Christopher Hacon, Claire Voisin, Ulrike Tillmann,  François Labourie Update: This was a great event with four great inspiring talks. Abel in Jerusalem, January 12, 2020 The Einstein Institute of mathematics is happy to host the Abel in Jerusalem Conference “Abel in … Continue reading

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