Some Updates

Jeff Kahn was in town: so we worked together also with Ehud Friedgut and Roy Meshulam (and others) quite intensively. Very nice! Stay tuned for a report! Polynomial Hirsch conjecture (polymath3): While the conjecture remains wide open there are some interesting developments. The conjecture asserts that the diameter of every d-dimensional polytope with n facets […]

Günter Ziegler: 1000$ from Beverly Hills for a Math Problem. (IPAM remote blogging.)

Scanned letter by Zadeh. (c) Günter M. Ziegler left-to-right: David Avis, Norman Zadeh,  Oliver Friedmann, and Russ Caflish (IPAM director). Photo courtesy Eddie Kim. Update: The slides for Friedmann’s talk are now available. The conference schedule page contains now the slides for most presentations. This post is authoured by Günter Ziegler with some help by David Avis. A […]

IPAM Remote Blogging: Santos-Weibel 25-Vertices Prismatoid and Prismatoids with large Width

Here is a web page by Christope Weibel on the improved counterexample. The IPAM webpage contains now slides of some of the lectures. Here are Santos’s slides. The last section contains some recent results on the “width of 5-prismatoids”  A prismatoid is a polytope with two facets containing all the vertices. The width of a prismatoid is the number […]

Emmanuel Abbe: Erdal Arıkan’s Polar Codes

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 coding theory. In his seminal work of 1948, Shannon had characterized the highest rate (speed […]

Roth’s Theorem: Tom Sanders Reaches the Logarithmic Barrier

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 . Roth proved that . Szemeredi and Heath-Brown improved it to for some 0″ src=”http://l.wordpress.com/latex.php?latex=c%3E0&bg=ffffff&fg=000000&s=0″ alt=”c>0″ /> […]

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

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 Festive Day: November 19 Today is a festive day. It was on this day, November […]

Subexponential Lower Bound for Randomized Pivot Rules!

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 if this is possible was an open problem for several decades. Here is a link […]

Budapest, Seattle, New Haven

Here we continue the previous post on Summer 2010 events in Reverse chronological order. Happy birthday Srac In the first week of August we celebrated Endre Szemeredi’s birthday. This was a very impressive conference. Panni, Endre’s wife, assisted by her four daughters, organized a remarkable exhibition by mathematicians who are also artists. Panni also organized […]

Polymath Reflections

Polymath is a collective open way of doing mathematics. It  started over Gowers’s blog with the polymath1 project that was devoted to the Density Hales Jewett problem. Since then we  had Polymath2 related to Tsirelson spaces in Banach space theory , an  intensive Polymath4 devoted to deterministically finding primes that took place on a special polymathblog, a miniPolymath leading to collectively solving an […]