During my visit to Imperial College London, I discussed topics related to groups and analysis with Professor Martin Liebeck and Professor Boguslaw Zegarlinski. Research with Professor Zegarlinski concerns infinite noncommutative Coxeter groups. With Professor Liebeck, and with Professor Shalev during his visit to Imperial College, I discussed properties of Cayley graphs of finite simple groups. Current research of Liebeck and Shalev on the girth of Cayley graphs of finite simple groups with respect to random generators is related to my recent work on mixing times on alternating groups again with respect to random generators. Problems concerning expansion for random generators are very deep and conjectured optimal results seem to be out of reach by current methods.
In addition, I had opportunities to discuss mathematics with researchers working at other UK universities. I gave seminars at Imperial, Oxford, Durham, York, Warwick, and conducted a graduate class on "Analysis and geometry on groups" at Imperial. I wrote a paper entitled "From Partial Differential Equations to Groups" related to talks I gave at the UK universities, which will appear in the volume "Analysis and Geometry on Graphs and Manifolds" published by Cambridge University Press.
I enjoyed my time at Imperial College very much.
Host: Professor Boguslaw Zegarlinski
