Last updated: 06 April 2010
I am not enthusiastic about mathematics lectures that consist mainly of reading notes, pdf files, or powerpoint presentations out loud, however well-written they may be. In this situation, the audience often gains little more than by private study of the supporting material. I prefer to hang lectures on a less rigid framework, by providing signposts, statements, references, examples, (and warnings!) for listeners to develop detailed proofs and interconnections for themselves. Hopefully, this happens through discussion and debate, in which I also like to participate.My aim is to follow this approach as closely as possible. The primary objective is therefore that members of the audience should acquire a feel for the subject that is appropriate to their mathematical sophistication, and develop the details by subsequent study of the clues and outlines that are presented in the lectures.
Things may, of course, work out less well than I would like!
I shall assume that participants are aware of (this certainly does not mean ‘have read’!) the following, and hope that they will have access to them during the week.
So far as more detailed knowledge is concerned, the following are basic, and will be assumed.
Everyone has their own favourite sources for this material. I often suggest that graduate students should consult the following.
More advanced background material, and an overview of activity around the planet, should be displayed on the Manchester Toric Topology page (if only I can find time to keep it up to date!)
I would prefer to give these lectures in Spanish, rather than assume that listeners understand English. Unfortunately, my vocabulary is about 20 words, including ‘hola’! However, if I set myself the task of learning a few additional words and phrases each day, maybe the audience can help me to improve during my visit.
As I complete my planning for each lecture, I shall add a corresponding pdf file below. This process is unlikely to be in chronological order, and the presentation may turn out to be rather unorthodox!