Title of the course: Incidence geometry and buildings
Instructor: Prof. Michel Lavrauw
Institution: Sabancı Ü.
Dates: 20-26 August 2018
Prerequisites: Basic algebra knowledge
Level: Advanced undergraduate, graduate
Abstract: Starting from basic point-line geometries satisfying a set of axioms, the students are introduced to projective planes, polar spaces, generalised polygons, and buildings. This course is about the relationship between groups and geometries, and is inspired by the work of Abel price winner Jacques Tits; in particular his work on the ecoding of the algebraic structure of linear groups in geometric terms. The course is intended as a gentle introduction to this theory, and accessible to any graduate student with basic algebra knowledge.
Most of the course will be based some of the chapters contained in the Handbook of Incidence Geometry [1] edited by Francis Buekenhout, a former PhD student of Jacques Tits. Below is a short description of the contents of [1].
This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively. More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.
[1] Handbook of Incidence Geometry, Buildings and Foundations (edited by F. Buekenhout) North Holland 1995.
Language: EN