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Convex Bodies, Lattices and Dimension
Colloquium| Speaker: | Roman Vershynin, University of Alberta & Pacific Institute for Mathematical Sciences |
| Location: | 693 Kerr |
| Start time: | Fri, Dec 20 2002, 4:10PM |
Description
Minkowski's Theorem, a central result in the geometry of numbers,
estimates the number of lattice points in a convex body K. In this talk,
we will count the number of lattice cells. The resulting counterpart of
Minkowski's theorem leads to a breakthrough in numerous problems in
combinatorics, convex geometry, random processes, functional analysis,
etc. I will describe a refcent solution to the entropy problem of
Talagrand, which implies a direct approach to Glivenko-Cantelli Problem in
probability, the general Bourgain-Tzafriri's principle of invertibility of
operators, the Harmonic Density Problem in harmonic analysis, a problem of
Alon et al. on the combinatorial dimension and some others.
3:45 Refreshments will be served before the talk in 551 Kerr Hall