Simultaneous Diophantine Approximations and a Conjecture of Minkowski

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Mathematics (CMC)

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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.


This lecture was given during an Introduction to Mathematical Research seminar series at the University of Texas at Austin in March 2006.

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© 2006 Lenny Fukshansky

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