Jeremy Champagne, Department of Pure Mathematics, University of Waterloo
"Geometry of numbers as a tool for Diophantine approximation"
Anybody who has taken a course on algebraic number theory, has probably seen Minkowski's convex body theorem as a mean to prove the finiteness of class groups. However, less people know about Minkowski's second convex body theorem, which gives much more insight into this problem of finding integer points with certain properties.
In this talk, we will a cover a short and intuitive proof of this result. This relates to Diophantine approximation notably through Parametric geometry of numbers, a complicated but beautiful subject which we will cover as best as we can.