Tag Archives: Peter Keevash

EKR, Steiner systems, association schemes, and all that

A great number of mathematical problems amount to looking in a large but highly structured graph, and finding a complete or null subgraph of largest possible size there. For a simple example, consider Latin squares of order n. One of … Continue reading

Posted in exposition | Tagged , , , , , , | Leave a comment

Synchronization and separation in the Johnson schemes

Today a paper by Mohammed Aljohani, John Bamberg and me went on the arXiv on this topic. Here is a brief summary of what it is about. Synchronization comes in several flavours, and the point of the paper is to … Continue reading

Posted in exposition, Uncategorized | Tagged , , , , | Leave a comment

Peter Keevash at IMS

This picture (courtesy of Sebi Cioabă) shows Peter Keevash with the diagram which illustrates the proof strategy for his theorem. Perhaps it will be helpful, especially to those who heard the lecture (or similar lectures elsewhere). Thanks Sebi!

Posted in exposition | Tagged , | Leave a comment

Keevash on triangle decompositions

Today Peter Keevash finished four and a half hours of lectures on his latest improvement of his result on the existence of designs. I have heard him talk on this before, but in a one-hour talk he had time to … Continue reading

Posted in Uncategorized | Tagged , , , | Leave a comment

Steiner systems

Following Peter Keevash’s asymptotic existence proof for Steiner systems, does anything remain to be done? I would say yes, it certainly does; here are a few thoughts about the open problems in this area. Existence We are looking for a … Continue reading

Posted in mathematics, open problems | Tagged , , , , , | 3 Comments

Steiner systems exist

A Steiner system S(t,k,n) is a collection of k-subsets (called “blocks”) of an n-set of “points” with the property that any t-set of points is contained in a unique block. To avoid trivial cases, we assume that t<k<n. Since the … Continue reading

Posted in mathematics | Tagged , , , | Leave a comment