Mini-course: Introduction to the Theory of Buildings

Time: to  Ngày 01/01/0001

Venue/Location:

Content:

Time: 9:30 – 11:30, from Monday 22 to Wednesday 31 December, 2014

Location: VIASM Lecture Hall C2.

Lecturer: Professor R. Weiss (Tufts University, USA)

Abstract:

Buildings are combinatorial/geometric structures introduced by Jacques Tits in the study of group theory. Buildings can be described entirely in the language of graph theory, and this is what we will do in these lectures. We will begin by introducing Coxeter groups and properties of their Cayley graphs. We will then define a building, give some examples and present some of the basic structural features of a building. In the remaining lectures, we will give an overview of Tits’ classification results for spherical and affine buildings and describe some of the algebraic structures which play a central role in these classifications.

Tentative program: The lectures will be given in the mornings, 9.30 – 11.30

1) Coxeter groups and their Cayley graphs (Dec. 22)

2) Roots, residues and convexity (Dec. 23)

3) Spherical Coxeter groups (Dec. 24)

4) Generalized polygons and buildings (Dec. 25)

5) Apartments (Dec. 26)

6) The Moufang property (Dec. 29)

7) The classification of spherical buildings (Dec. 30)

Affine buildings (Dec. 31).

References:

(1) Peter Abramenko and Kenneth S. Brown, “Buildings”, Springer, 2008.

(2) Mark Ronan, “Lectures on Buildings”, University of Chicago Press, 2009.

(3) Jacques Tits, “Buildings of Spherical Type and Finite BN-Pairs”, Springer Lecture Notes in Math. 386, 1974.

(4) Jacques Tits and Richard M. Weiss, “Moufang Polygons”, Springer, 2002.

(5) Richard M. Weiss, The Structure of Spherical Buildings, Princeton University Press, 2003.

(6) Richard M. Weiss, The Structure of Affine Buildings, Princeton University Press, 2009.

Registration:

Please fill in the registration form below your contact information. Deadline for registration: 18/12/2014.