Groups of finite Morley rank can be viewed as infinite groups equipped with a notion of dimension. In this talk, we’ll enter the subject rapidly via the axiomatic definition introduced by Borovik, discuss some of the major tools used to study these groups (using only very basic model theory), and present current avenues of research along with major obstructions. Recent study has involved tools inspired by finite group theory, algebraic geometry, Lie groups, and model theory - so there should be something of interest to (almost) everyone!
A Brief Survey of Groups of Finite Morley Rank