Simultaneous Diophantine Approximations and a Conjecture of Minkowski
This is an introductory expository lecture of elementary level. We start with a brief overview of some classical results in Diophantine approximations, such as Dirichlet's theorem. We then discuss a certain higher dimensional analogue of it, namely approximation of points in a Euclidean space by points of a unimodular lattice. In this direction, we give an overview of the famous conjecture of Minkowski and some of the very exciting recent developments of C. McMullen on this subject.
© 2006 Lenny Fukshansky
Fukshansky, Lenny. "Simultaneous Diophantine Approximations and a Conjecture of Minkowski." Introduction to Mathematical Research seminar series, University of Texas at Austin, Austin, Texas. March 2006.