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 Polymath 10 post 6: The ErdosRado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
 Polymath 10 Emergency Post 5: The ErdosSzemeredi Sunflower Conjecture is Now Proven.
 Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
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 The Erdős Szekeres polygon problem – Solved asymptotically by Andrew Suk.
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 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
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 The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond
 Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
 In how many ways you can chose a committee of three students from a class of ten students?
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Monthly Archives: December 2009
Randomness in Nature
Here is an excellent question asked by Liza on “Mathoverflow“. What is the explanation of the apparent randomness of highlevel phenomena in nature? For example the distribution of females vs. males in a population (I am referring to randomness in terms … Continue reading
Posted in Probability
Tagged foundation of probability, Math Overflow, Philosophy, Physics, Randomness
22 Comments
Midrasha News
Our Midrasha is going very very well. There are many great talks, mostly very clear and helpful. Various different directions which interlace very nicely. Some moving new mathematical breakthroughs; very few fresh from the oven. Tomorrow is the last day. Update: I will try … Continue reading
Joe Malkevitch: Why Planar Graphs are so Exceptional
Not only do interesting questions arise by considering the special class of planar graphs but additional special issues arise when one considers a specific plane drawing of a planar graph. This is because when a graph is drawn in … Continue reading
Posted in Combinatorics, Guest blogger
6 Comments
When Noise Accumulates
I wrote a short paper entitled “when noise accumulates” that contains the main conceptual points (described rather formally) of my work regarding noisy quantum computers. Here is the paper. (Update: Here is a new version, Dec 2010.) The new exciting innovation in computer … Continue reading
Plans for polymath3
Polymath3 is planned to study the polynomial Hirsch conjecture. In order not to conflict with Tim Gowers’s next polymath project which I suppose will start around January, I propose that we will start polymath3 in mid April 2010. I plan to write a … Continue reading
Four Derandomization Problems
Polymath4 is devoted to a question about derandomization: To find a deterministic polynomial time algorithm for finding a kdigit prime. So I (belatedly) devote this post to derandomization and, in particular, the following four problems. 1) Find a deterministic algorithm for primality 2) Find … Continue reading
Posted in Computer Science and Optimization, Probability
Tagged derandomization, polymath4, Randomness
7 Comments
Why are Planar Graphs so Exceptional
Harrison Brown asked the problem “Why are planar graphs so exceptional” over mathoverflow, and I was happy to read it since it is a problem I have often thought about over the years, as I am sure have many combinatorialsists and graph … Continue reading
Posted in Combinatorics, Convex polytopes
2 Comments