Dave Witte Morris

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...

We will discuss a few basic properties of "arithmetic groups," which are certain groups of n-by-n matrices with integer entries. By definition, the subject combines algebra (group theory and matrices) with number theory (the integers), but it also...