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 Alexander A. Gaifullin: Many 27vertex Triangulations of Manifolds Like the Octonionic Projective Plane (Not Even One Was Known Before).
 Answer to Test Your Intuition 50: Detecting a Deviator
 To cheer you up in difficult times 36: The Immense Joy of Fake Reverse Parking
 Ordinary computers can beat Google’s quantum computer after all
 Test Your Intuition 50. TwoPlayer Random Walk; Can You Detect Who Did Not Follow the Rules?
 ICM 2022. Kevin Buzzard: The Rise of Formalism in Mathematics
 ICM 2022: Langlands Day
 ICM 2022 awarding ceremonies (1)
 ICM 2022 Virtual Program, Live events, and Dynamics Week in Jerusalem
Top Posts & Pages
 How Large can a Spherical Set Without Two Orthogonal Vectors Be?
 ICM 2022: Langlands Day
 Amazing: Hao Huang Proved the Sensitivity Conjecture!
 ICM 2022. Kevin Buzzard: The Rise of Formalism in Mathematics
 Answer to Test Your Intuition 50: Detecting a Deviator
 Amazing: Karim Adiprasito proved the gconjecture for spheres!
 Peter Keevash: More and Easier Designs!
 Raigorodskii's Theorem: Follow Up on Subsets of the Sphere without a Pair of Orthogonal Vectors
 Alexander A. Gaifullin: Many 27vertex Triangulations of Manifolds Like the Octonionic Projective Plane (Not Even One Was Known Before).
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Monthly Archives: February 2019
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 gconjecture on how to move from vertexdecomposable 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 Brad Rodgers, Dan Romik, Don Zagier, Ken Ono, Larry Rolen, Michel Griffin, polymath15, Terry Tao, Zeta function
4 Comments
Karim Adiprasito: The gConjecture for Vertex Decomposible Spheres
J Scott Provan (site) The following post was kindly contributed by Karim Adiprasito. (Here is the link to Karim’s paper.) Update: See Karim’s comment on the needed ideas for extend the proof to the general case. See also in the … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry, Guest blogger
Tagged gconjecture, J Scott Provan, Karim Adiprasito, Leonid Gurvits, Lou Billera
9 Comments
Attila Por’s Universality Result for Tverberg Partitions
In this post I would like to tell you about three papers and three theorems. I am thankful to Moshe White and Imre Barany for helpful discussions. a) Universality of vector sequences and universality of Tverberg partitions, by Attila Por; Theorem … Continue reading
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
Extremal Combinatorics V: POSETS
This is the remaining post V on partially ordered sets of my series on extremal combinatorics (I,II,III,IV,VI). We will talk here about POSETS – partially ordered sets. The study of order is very important in many areas of mathematics starting … Continue reading
Konstantin Tikhomirov: The Probability that a Bernoulli Matrix is Singular
Konstantin Tikhomirov An old problem in combinatorial random matrix theory is cracked! Singularity of random Bernoulli matrices by Konstantin Tikhomirov Abstract: For each , let be an n×n random matrix with independent ±1 entries. We show that P( is singular}=, … Continue reading