- Many triangulated three-spheres!
- NatiFest is Coming
- More around Borsuk
- Analysis of Boolean Functions – Week 7
- Analysis of Boolean Functions week 5 and 6
- Real Analysis Introductory Mini-courses at Simons Institute
- Analysis of Boolean Functions – week 4
- Polymath 8 – a Success!
- Analysis of Boolean Functions – Week 3
Top Posts & Pages
- Polymath 8 - a Success!
- The Kadison-Singer Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
- Believing that the Earth is Round When it Matters
- Analysis of Boolean Functions
- NatiFest is Coming
- יופיה של המתמטיקה
- Analysis of Boolean Functions - week 1
- Greg Kuperberg: It is in NP to Tell if a Knot is Knotted! (under GRH!)
- Extremal Combinatorics IV: Shifting
Category Archives: Open problems
Problem: Let P be a polytope in with n facets. Is it always true that P can be covered by n sets of smaller diameter? I also asked this question over mathoverflow, with some background and motivation.
Satoshi Murai and Eran Nevo have just proved the 1971 generalized lower bound conjecture of McMullen and Walkup, in their paper On the generalized lower bound conjecture for polytopes and spheres . Let me tell you a little about it. … Continue reading
This post follows a recent paper On sunflowers and matrix multiplication by Noga Alon, Amir Spilka, and Christopher Umens (ASU11) which rely on an earlier paper Group-theoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading
MathOverflow is a remarkable recent platform for research level questions and answers in mathematics. Joe O’Rourke have asked over MO wonderful questions. (Here is a link to the questions) Many of those questions can be the starting point of a research … Continue reading
In a recent post I mentioned quite a few remarkable recent developments in combinatorics. Let me mention a couple more. Independent sets in regular graphs A challenging conjecture by Noga Alon and Jeff Kahn in graph theory was about the number of … Continue reading
Cocycles Definition: A -cocycle is a collection of -subsets such that every -set contains an even number of sets in the collection. Alternative definition: Start with a collection of -sets and consider all -sets that contain an odd number of members … Continue reading
The Complexity of Zero-Sum Stochastic Games with Perfect Information Is there a polynomial time algorithm for chess? Well, if we consider the complexity of chess in terms of the board size then it is fair to think that the answer is … Continue reading
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
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
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