# Mathematical Sciences Research Institute

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# Seminar

GFA Main Seminar: Fine approximation of convex bodies by polytope October 05, 2017 (02:00 PM PDT - 03:00 PM PDT)
Parent Program: Geometric Functional Analysis and Applications MSRI: Simons Auditorium
Speaker(s) Dimitry Ryabogin (Kent State University)
Description No Description
Video
This is a joint result with M\'arton Nasz\'odi and Fedor Nazarov. We prove that for every convex body $K$ with the center of mass at the origin and every $\varepsilon\in \left(0,\frac{1}{2}\right)$, there exists a convex polytope $P$ with at most $e^{O(d)}\varepsilon^{-\frac{d-1}{2}}$ vertices such that $(1-\varepsilon)K\subset P\subset K$.