Search Results for: g-conjecture

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

Four Great Numberphile Graph Theory Videos

A quick link to our previous post: Gil Bor, Luis Hernández-Lamoneda, Valentín Jiménez-Desantiago, and Luis Montejano-Peimbert: On the isometric conjecture of Banach.   We have mentioned the Numberphile video channel before (here, and here, and here). It has amazing videos for … Continue reading

Posted in Combinatorics | Tagged , , , , , | Leave a comment

Isabella Novik and Hailun Zheng: Neighborly centrally symmetric spheres exist in all dimensions!

A tweet-long summary: The cyclic polytope is wonderful and whenever we construct an analogous object we are happy. Examples: Neighborly cubic polytopes; The amplituhedron; and as of last week, the Novik-Zheng new construction of neighborly centrally symmetric spheres! At last: … Continue reading

Posted in Combinatorics, Convexity | Tagged , | Leave a comment

Dan Romik Studies the Riemann’s Zeta Function, and Other Zeta News.

Updates to previous posts: Karim Adiprasito expanded in a comment to his post on the g-conjecture on how to move from vertex-decomposable spheres to general spheres. Some photos were added to the post: Three pictures. Dan Romik on the Zeta … Continue reading

Posted in Number theory, Updates | Tagged , , , , , , , , | 4 Comments

Exciting Beginning-of-the-Year Activities and Seminars.

Let me mention two talks with very promising news by friends of the blog, Karim Adiprasito and Noam Lifshitz. As always, with the beginning of the academic year there are a lot of exciting activities,  things are rather hectic around,  … Continue reading

Posted in Combinatorics, Geometry, Probability | Tagged , , , , | 3 Comments

Ricky and Branko

Two dear friends, and great geometers, Ricky Pollack and Branko Grünbaum  passed away a few weeks ago. Ricky was a close friend that both Mazi my wife and I loved, and we were both fascinated by his wisdom, charm and … Continue reading

Posted in Combinatorics, Convexity, Geometry, Obituary | Tagged , | 3 Comments

Around the Garsia-Stanley’s Partitioning Conjecture

  Art Duval, Bennet Goeckner, Carly Klivans, and Jeremy Martin found a counter example to the Garsia-Stanley partitioning conjecture for Cohen-Macaulay complexes. (We mentioned the conjecture here.)  Congratulations Art, Bennet, Carly and Jeremy!  Art, Carly, and Jeremy also wrote an article on the … Continue reading

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

Convex Polytopes: Seperation, Expansion, Chordality, and Approximations of Smooth Bodies

I am happy to report on two beautiful results on convex polytopes. One disproves an old conjecture of mine and one proves an old conjecture of mine. Loiskekoski and Ziegler: Simple polytopes without small separators. Does Lipton-Tarjan’s theorem extends to high … Continue reading

Posted in Combinatorics, Convex polytopes | Tagged , , , , , | 3 Comments

Updates and plans III.

Update on the great Noga’s Formulas competition. (Link to the original post, many cash prizes are still for grab!) This is the third “Updates and plans post”. The  first one was from 2008 and the  second one from 2011. Updates: Combinatorics and … Continue reading

Posted in Combinatorics, Conferences, Updates | 13 Comments

Combinatorics and More – Greatest Hits

Combinatorics and More’s Greatest Hits First Month Combinatorics, Mathematics, Academics, Polemics, … Helly’s Theorem, “Hypertrees”, and Strange Enumeration I (There were 3 follow up posts:) Extremal Combinatorics I: Extremal Problems on Set Systems (There were 4 follow up posts II ; III; IV; VI) Drachmas Rationality, Economics and … Continue reading

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