Monthly Archives: February 2019

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

Posted on February 28, 2019 by Gil Kalai

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

Karim Adiprasito: The g-Conjecture for Vertex Decomposible Spheres

Posted on February 23, 2019 by Gil Kalai

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 , , , , | 9 Comments

Fix a Horse Race…

Posted on February 20, 2019 by Gil Kalai

GK (2019): Can you base world economy on horse races? Here is an old unpublished draft from 2008 that I did not complete, which was  inspired by the  economic crisis at that time. (It also felt a little over the … Continue reading →

Posted in Economics, Games, Rationality, Taxi-and-other-stories | Tagged , , , | Leave a comment

Attila Por’s Universality Result for Tverberg Partitions

Posted on February 16, 2019 by Gil Kalai

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 →

Posted in Combinatorics, Convexity | Tagged , , , , , , , | 9 Comments

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

Posted on February 15, 2019 by Gil Kalai

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 →

Posted in Algebra, Combinatorics, Geometry, Number theory | Tagged , , , , , , , | 2 Comments

Extremal Combinatorics V: POSETS

Posted on February 5, 2019 by Gil Kalai

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 →

Posted in Combinatorics | Tagged , , , , , , , , , | 6 Comments

Konstantin Tikhomirov: The Probability that a Bernoulli Matrix is Singular

Posted on February 2, 2019 by Gil Kalai

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 →

Posted in Combinatorics, Probability | Tagged | 4 Comments