Title: Calculating probabilities in matrix groups over finite fields
Lecturer: Peter M Neumann (Oxford)
Abstract: These lectures will be about the statistics describing the
distribution of various kinds of elements in matrix groups over finite
fields. They will focus on such examples as the probability of a matrix
being separable, or irreducible, or cyclic, or eigenvalue-free. One
strong motivation is that knowledge of some of these probabilities helps
us to design and analyse non-deterministic algorithms for computation in
the relevant groups. The three lectures will be designed as three
surveys. One will be a survey of what we would like to know. Another a
survey of methods, focussing mainly on cycle indices and generating
function methods. The third will be a survey of results.
Prerequisites: undergraduate algebra together with a little knowledge of
classical groups over finite fields (as in, for example, D E Taylor, The
Geometry of the Classical Groups); standard undergraduate complex
analysis.