Just returning from a cozy two days discrete-math workshop in Marburg. A very nice mixture of participants and topics. The title of my talk was “Helly theorem, hypertrees and strange enumeration” and I plan to blog about it sometime soon. A few hours before taking off, Aner Shalev told me that a 1951 conjecture by Ore asserting that every element in a non abelian finite simple group is a commutator have just been proved by a group of four researchers – Aner himself and Liebeck, O’Brien and Tiep. (Ore himself proved that for every element is a commutator.) The basis for a very complicated inductive proof required computer works and the final OK came four hours before Aner gave a lecture about it!
The talks in Marburg were very interesting.
Day 1:Enumerative combinatorics techniques and results related to the asymptotic conjectured formula for the number of self avoiding random walks (a holy grail in statistical mechanics); Continue reading