Topology Seminar: Introduction to Ratner's Theorems on Unipotent Flows

  • Date: 03/31/2010
Dave Witte Morris (University of Lethbridge)

University of British Columbia


Let f be the obvious covering map from Euclidean n-space to the n-torus. It is well known that if L is any straight line in n-space, then the closure of f(L) is a very nice submanifold of the n-torus. In 1990, Marina Ratner proved a beautiful generalization of this observation that replaces Euclidean space with any Lie group G, and allows L to be any subgroup of G that is "unipotent." We will discuss the statement of Ratner's Theorem, and a few of its important consequences. Topological and geometric aspects will be emphasized, while algebraic technicalities will be pushed to the background.


3:00 - 4:00pm, WMAX 110.