Hall 123

Geometry of Numbers and Diophantine Approximation

Wolfgang Schmidt

University of Colorado

We will begin by recalling basic facts on the Geometry of Numbers, as developed by Minkowski and Mahler. These involve the "successive
minima" of a lattice with respect to a convex body. We next will introduce new work on "parametric Geometry of Numbers', where the
convex body is transformed by a family of linear maps. As a consequence, we will get new insights on an area of Diophantine Approximations pioneered by Khintchine and Jarnik. In particular, we
will compare regular and uniform approximation exponents.