Monthly Archives: February 2019

Fix a Horse Race…

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 Here is an old unpublished draft from 2008 that I did not complete, which was  inspired by the  economic crisis at that time.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

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 , , , , , , , | 4 Comments

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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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

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

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

Posted in Combinatorics, Probability | Tagged | 1 Comment