Category Archives: Algebra

Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska: Universal optimality of the E8 and Leech lattices and interpolation formulas

Henry Cohn A follow up paper on the tight bounds for sphere packings in eight and 24 dimensions. (Thanks, again, Steve, for letting me know.) For the 2016 breakthroughs see this post, this post of John Baez, this article by Erica Klarreich on … Continue reading

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Interesting Times in Mathematics: Enumeration Without Numbers, Group Theory Without Groups.

Lie Theory without Groups: Enumerative Geometry and Quantization of Symplectic Resolutions Our 21th Midrasha (school) IIAS, January 7 – January 12, 2018 Jerusalem Enumerative Geometry Beyond Numbers MSRI,  January 16, 2018 to May 25, 2018 Abstract for the Midrasha

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AlexFest: 60 Faces of Groups

  Ladies and gentlemen, A midrasha (school) in honor of Alex Lubotzky’s 60th birthday will take place from November 6 – November 11, 2016 at the Israel Institute for Advanced Studies, the Hebrew University of Jerusalem. Don’t miss the event! And … Continue reading

Posted in Algebra, Combinatorics, Conferences, Updates | Tagged | 4 Comments

The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond

A quick schematic road-map to these new geometric objects. The  positroidron can be seen as a cellular structure on the nonnegative Grassmanian – the part of the real Grassmanian G(m,n) which corresponds to m by n matrices with all m by … Continue reading

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From Peter Cameron’s Blog: The symmetric group 3: Automorphisms

Originally posted on Peter Cameron's Blog:
No account of the symmetric group can be complete without mentioning the remarkable fact that the symmetric group of degree n (finite or infinite) has an outer automorphism if and only if n=6.…

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TYI 25: The Automorphism Group of the Symmetric Group

True or False: The group of automorphisms of the symmetric group , n ≥ 3 is itself.  

Posted in Algebra, Test your intuition | Tagged , | 7 Comments

Test your intuition 24: Which of the following three groups is trivial

Martin Bridson We have three finitely presented groups A is generated by two generators a and b and one relation   B is generated by three generators a, b, c and three relations ,    . C is generated by four generators a, b, c, d … Continue reading

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Andrei Zelevinsky passed away a week ago on April 10, 2013, shortly after turning sixty. Andrei was a great mathematician and a great person. I first met him in a combinatorics conference in Stockholm 1989. This was the first major … Continue reading

Posted in Algebra, Combinatorics, Obituary | Tagged | 5 Comments

Course Announcement: High Dimensional Expanders

Alex Lubotzky and I  are running together a year long course at HU on High Dimensional Expanders. High dimensional expanders are simplical (and more general) cell complexes which generalize expander graphs. The course will take place in Room 110 of the mathematics building … Continue reading

Posted in Algebra, Combinatorics, Geometry, Teaching | Tagged | 2 Comments

Octonions to the Rescue

Xavier Dahan and Jean-Pierre Tillich’s Octonion-based Ramanujan Graphs with High Girth. Update (February 2012): Non associative computations can be trickier than we expect. Unfortunately, the paper by Dahan and Tillich turned out to be incorrect. Update: There is more to … Continue reading

Posted in Algebra, Combinatorics, Computer Science and Optimization, Open problems, Physics | Tagged , , , | 12 Comments