Monthly Archives: November 2010

Polynomial Hirsch Conjecture 5: Abstractions and Counterexamples.

Posted on November 28, 2010 by Gil Kalai

This is the 5th research thread of polymath3 studying the polynomial Hirsch conjecture. As you may remember, we are mainly interested in an abstract form of the problem about families of sets. (And a related version about families of multisets.) The … Continue reading →

Posted in Open problems, Polymath3 | Tagged , | 60 Comments

Analysis of Boolean Functions

Posted on November 28, 2010 by Gil Kalai

I discovered a vidiotaped lecture I gave at the Open University on the 3rd Israeli Theory Day. Enjoy! http://www.youtube.com/watch?v=xbJe7ioCISM Posts related to this lecture: Noise Stability and threshold circuits; Noise stability lecture and tales;  Nati’s influence.

Posted in Computer Science and Optimization | 3 Comments

Emmanuel Abbe: Erdal Arıkan’s Polar Codes

Posted on November 25, 2010 by Gil Kalai

Click here for the most recent polymath3 research thread. A new thread is comming soon. Emmanuel Abbe and Erdal Arıkan This post is authored by Emmanuel Abbe A new class of codes, called polar codes, recently made a breakthrough in … Continue reading →

Posted in Information theory, Probability | Tagged , | 17 Comments

Roth’s Theorem: Tom Sanders Reaches the Logarithmic Barrier

Posted on November 24, 2010 by Gil Kalai

Click here for the most recent polymath3 research thread. I missed Tom by a few minutes at Mittag-Leffler Institute a year and a half ago Suppose that  is a subset of of maximum cardinality not containing an arithmetic progression of length 3. Let . … Continue reading →

Posted in Combinatorics, Open problems | Tagged , , , , , | 13 Comments

János Pach: Guth and Katz’s Solution of Erdős’s Distinct Distances Problem

Posted on November 20, 2010 by Gil Kalai

Click here for the most recent polymath3 research thread. Erdős and Pach celebrating another November day many years ago. The Wolf disguised as Little Red Riding Hood. Pach disguised as another Pach. This post is authored by János Pach A … Continue reading →

Posted in Combinatorics, Geometry, Guest blogger, Open problems | Tagged , | 14 Comments

Aaronson and Arkhipov’s Result on Hierarchy Collapse

Posted on November 17, 2010 by Gil Kalai

Scott Aaronson gave a thought-provoking lecture in our Theory seminar three weeks ago.  (Actually, this was eleven months ago.) The slides are here . The lecture discussed two results regarding the computational power of quantum computers. One result from this paper gives an … Continue reading →

Posted in Computer Science and Optimization, Physics, Quantum | Tagged , , , , , | 15 Comments

Octonions to the Rescue

Posted on November 15, 2010 by Gil Kalai

Xavier Dahan and Jean-Pierre Tillich’s Octonion-based Ramanujan Graphs with High Girth. Update (February 2012): Non associative computations can be trickier than we expect. Unfortunately, the paper by Dahan and Tillich turned out to be incorrect. Update: There is more to … Continue reading →

Posted in Algebra, Combinatorics, Computer Science and Optimization, Open problems, Physics | Tagged , , , | 12 Comments

Subexponential Lower Bound for Randomized Pivot Rules!

Posted on November 9, 2010 by Gil Kalai

Oliver Friedmann, Thomas Dueholm Hansen, and Uri Zwick have managed to prove subexponential lower bounds of the form for the following two basic randomized pivot rules for the simplex algorithm! This is the first result of its kind and deciding … Continue reading →

Posted in Computer Science and Optimization, Convex polytopes, Games | Tagged , | 11 Comments