*This post is authored by* *Karim Adiprasito*

The past months have seen some exciting progress on diameter bounds for polytopes and polytopal complexes, both in the negative and in the positive direction. 1,378 more words

*This post is authored by* *Karim Adiprasito*

The past months have seen some exciting progress on diameter bounds for polytopes and polytopal complexes, both in the negative and in the positive direction. 1,378 more words

Inspired by an article in the New Scientist I am returning to a favourite subject – whether P = NP and what the implications would be in the (unlikely) case that this were so. 749 more words

This is a new polymath3 research thread. Our aim is to tackle the polynomial Hirsch conjecture which asserts that **there is a polynomial upper bound for the diameter of graphs of -dimensional polytopes with facets.** 702 more words

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. 1,179 more words

**So where are we?** I guess we are trying all sorts of things, and perhaps we should try even more things. I find it very difficult to choose the more promising ideas, directions and comments as Tim Gowers and Terry Tao did so effectively in Polymath 1,4 and 5. 754 more words

Here we start the second research thread about the polynomial Hirsch conjecture. I hope that people will feel as comfortable as possible to offer ideas about the problem. 207 more words

Gil Kalai has officially started the Polymath3 project (Polynomial Hirsch conjecture) with a research thread at his blog.

The original aim of this project is to prove the polynomial Hirsch conjecture, which is a conjecture in the combinatorial geometry of polytopes. 180 more words