Algebraic groups, geometric invariant theory and actions on spherical buildings
Aberdeen University 全年开放
相关专业：Mathematics
详细信息
Project Deion
Group theory is the mathematical study of symmetry. Algebraic groups are certain groups of matrices with entries coming from a field such as the real numbers, the complex numbers or the integers modulo a prime. They are important in many areas of pure mathematics including number theory, representation theory and the theory of buildings. Their study combines ideas from algebraic geometry (the geometry of polynomials) and group theory.
In recent years some powerful geometric techniques were introduced to prove results about algebraic groups and related mathematical objects. The aim of this project is to investigate new applications of these techniques to the structure of algebraic groups and the spaces that they act on. Some possible directions for research include geometric invariant theory, spherical buildings and the subgroup structure of algebraic groups over non-algebraically closed fields.
The successful candidate will have or expect to have a UK Honours Degree at 2.1 (or equivalent) in Mathematics.
Knowledge of: Algebra, group theory. Some knowledge of algebraic geometry would be useful but is not essential.
