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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 |

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