The course will take place on Mondays from 14.00 to 16.00. First lecture on Monday 14/10/19 and it will continue for 8 weeks.
You can contact me at marcelo.demartino 'at' maths.ox.ac.uk.
Buildings are purely combinatorial objects that, as topological spaces, are cell complexes made up out of smaller complexes, the so-called apartments. When a group G acts nicely on the building, information about the structure and the representation theory of G can be inferred from this action. The lectures will be divided into two parts:
The main references for the course will be:
Another valuable references are:
Specially for the second part, aside from the above-mentioned books, the monumental treatise of Bruhat and Tits, entitled "Groupes Reductifs sur un Corps Local", parts I, II and III are, of course, very relevant. But we also single out:
These are the lecture notes for the course and here are the pictures. In case you spot typos/mistakes in the text, or has any remarks/questions, please drop me a line. Last update: 09 December 2019.
Here are the slides to the course:
These are the exercise sheets for the course. If you need some sort of evaluation, please complete these exercises and send it to marcelo.demartino 'at' maths.ox.ac.uk until Wednesday of week 8.