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 Test Your Intuition about the AlonTarsi Conjecture
 Thilo Weinert: Transfinite Ramsey Numbers
 Timothy Chow Launched Polymath12 on Rota Basis Conjecture and Other News
 Proof By Lice!
 The seventeen camels riddle, and Noga Alon’s camel proof and algorithms
 Edmund Landau and the Early Days of the Hebrew University of Jerusalem
 Boolean Functions: Influence, Threshold, and Noise
 Laci Babai Visits Israel!
 Polymath10 conclusion
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 News (mainly polymath related)
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
 Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
 Test Your Intuition about the AlonTarsi Conjecture
 Emmanuel Abbe: Erdal Arıkan's Polar Codes
 Believing that the Earth is Round When it Matters
 The KadisonSinger Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
 Extremal Combinatorics IV: Shifting
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Category Archives: Open problems
The Polynomial Hirsch Conjecture: Discussion Thread, Continued
Here is a link for the justposted paper Diameter of Polyhedra: The Limits of Abstraction by Freidrich Eisenbrand, Nicolai Hahnle, Sasha Razborov, and Thomas Rothvoss. And here is a link to the paper by Sandeep Koranne and Anand Kulkarni “The dstep Conjecture is Almost true” – … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Convex polytopes, Hirsch conjecture
16 Comments
(Eran Nevo) The gConjecture III: Algebraic Shifting
This is the third in a series of posts by Eran Nevo on the gconjecture. Eran’s first post was devoted to the combinatorics of the gconjecture and was followed by a further post by me on the origin of the gconjecture. … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged gconjecture, Shifting
3 Comments
The Polynomial Hirsch Conjecture: Discussion Thread
This post is devoted to the polymathproposal about the polynomial Hirsch conjecture. My intention is to start here a discussion thread on the problem and related problems. (Perhaps identifying further interesting related problems and research directions.) Earlier posts are: The polynomial Hirsch … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Hirsch conjecture, Polytopes
115 Comments
Polymath4 – Finding Primes Deterministically – is On Its Way
After two long and interesting discussion threads polymath4, devoted to finding deterministically large prime numbers, is on its way on the polymath blog.
The Polynomial Hirsch Conjecture – How to Improve the Upper Bounds.
I can see three main avenues toward making progress on the Polynomial Hirsch conjecture. One direction is trying to improve the upper bounds, for example, by looking at the current proof and trying to see if it is wasteful and if so where … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Discussion, Hirsch conjecture
14 Comments
The Polynomial Hirsch Conjecture, a Proposal for Polymath3 (Cont.)
The Abstract Polynomial Hirsch Conjecture A convex polytope is the convex hull of a finite set of points in a real vector space. A polytope can be described as the intersection of a finite number of closed halfspaces. Polytopes have … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Hirsch conjecture, Polymath proposals
5 Comments
The Polynomial Hirsch Conjecture: A proposal for Polymath3
This post is continued here. Eddie Kim and Francisco Santos have just uploaded a survey article on the Hirsch Conjecture. The Hirsch conjecture: The graph of a dpolytope with n vertices facets has diameter at most nd. We devoted several … Continue reading
Raigorodskii’s Theorem: Follow Up on Subsets of the Sphere without a Pair of Orthogonal Vectors
Andrei Raigorodskii (This post follows an email by Aicke Hinrichs.) In a previous post we discussed the following problem: Problem: Let be a measurable subset of the dimensional sphere . Suppose that does not contain two orthogonal vectors. How large … Continue reading
How Large can a Spherical Set Without Two Orthogonal Vectors Be?
The problem Witsenhausen’s Problem (1974): Let be a measurable subset of the dimensional sphere . Suppose that does not contain two orthogonal vectors. How large can the dimensional volume of be? A Conjecture Conjecture: The maximum volume is attained … Continue reading
Posted in Open problems
4 Comments
The CapSet Problem and FranklRodl Theorem (C)
Update: This is a third of three posts (part I, part II) proposing some extensions of the cap set problem and some connections with the Frankl Rodl theorem. Here is a post presenting the problem on Terry Tao’s blog (March 2007). Here … Continue reading
Posted in Combinatorics, Open problems
Tagged Cap sets, FranklRodl theorem, polymath1
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