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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
 Game Theory 2021
 Past and Future Events
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
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 Bálint Virág: Random matrices for Russ
 Telling a Simple Polytope From its Graph
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Tag Archives: Richard Stanley
Cheerful news in difficult times: Richard Stanley wins the Steele Prize for lifetime achievement!
Richard Stanley, a most famous and influential mathematician in my area of combinatorics, the master of finding deep connections between combinatorics and other areas of pure mathematics, and my postdoctoral advisor, has just won the Steele prize for lifetime achievement, … Continue reading
Beyond the gconjecture – algebraic combinatorics of cellular spaces I
The gconjecture for spheres is surely the one single conjecture I worked on more than on any other, and also here on the blog we had a sequence of posts about it by Eran Nevo (I,II,III,IV). Here is a great … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry
Tagged Anders Bjorner, Bob MacPherson, Carl Lee, Ed Swartz, Eran Nevo, gconjecture, Günter Ziegler, Isabella Novik, June Huh, Kalle Karu, Karim Adiprasito, KazhdanLustig polynomials, Lou Billera, Marge Bayer, Peter McMullen, Richard Stanley, Ron Adin, Satoshi Murai, Tom Braden
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Happy Birthday Richard Stanley!
This week we are celebrating in Cambridge MA , and elsewhere in the world, Richard Stanley’s birthday. For the last forty years, Richard has been one of the very few leading mathematicians in the area of combinatorics, and he found deep, profound, and … Continue reading
Richard Stanley: How the Proof of the Upper Bound Theorem (for spheres) was Found
The upper bound theorem asserts that among all ddimensional polytopes with n vertices, the cyclic polytope maximizes the number of facets (and kfaces for every k). It was proved by McMullen for polytopes in 1970, and by Stanley for general triangulations … Continue reading
(Eran Nevo) The gConjecture II: The Commutative Algebra Connection
Richard Stanley This post is authored by Eran Nevo. (It is the second in a series of five posts.) The gconjecture: the commutative algebra connection Let be a triangulation of a dimensional sphere. Stanley’s idea was to associate with a ring … Continue reading
(Eran Nevo) The gConjecture I
This post is authored by Eran Nevo. (It is the first in a series of five posts.) Peter McMullen The gconjecture What are the possible face numbers of triangulations of spheres? There is only one zerodimensional sphere and it consists … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged Carl Lee, Eran Nevo, face rings, gconjecture, Lou Billera, Peter McMullen, Polytopes, Richard Stanley
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