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 Past and Future Events
 Joshua Hinman proved Bárány’s conjecture on face numbers of polytopes, and Lei Xue proved a lower bound conjecture by Grünbaum.
 Amazing: Jinyoung Park and Huy Tuan Pham settled the expectation threshold conjecture!
 Combinatorial Convexity: A Wonderful New Book by Imre Bárány
 Chaim EvenZohar, Tsviqa Lakrec, and Ran Tessler present: The Amplituhedron BCFW Triangulation
 Ehud Friedgut: How many cubes of 2×2×2 fit into a box of size 8×4×3? (TYI 49)
 Is HQCA Possible? A conversation with Michael Brooks
 To cheer you up in difficult times 35 combined with Test Your Intuition 48: Alef’s corner – Jazz and Math
 Reflections: On the Occasion of Ron Adin’s and Yuval Roichman’s Birthdays, and FPSAC 2021
Top Posts & Pages
 Amazing: Jinyoung Park and Huy Tuan Pham settled the expectation threshold conjecture!
 Joshua Hinman proved Bárány's conjecture on face numbers of polytopes, and Lei Xue proved a lower bound conjecture by Grünbaum.
 TYI 30: Expected number of Dice throws
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Game Theory 2021
 Telling a Simple Polytope From its Graph
 A sensation in the morning news  Yaroslav Shitov: Counterexamples to Hedetniemi's conjecture.
 Bálint Virág: Random matrices for Russ
 Past and Future Events
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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