From: Brenda Cook (brenda@math.missouri.edu)
Date: Mon Sep 25 2006 - 08:10:48 CDT
COLLOQUIUM
University of Missouri-Columbia
Department of Mathematics
Prof Elisabeth Werner
Case Western Reserve University
Approximation of the Euclidean ball by polytopes
We discuss the following new result:
There is a constant $c$ such that for every $n\in\mathbb N$
there is a $N_{n}$ so that for every
$N\geq N_{n}$ there is a polytope $P_{}$ in $\mathbb R^{n}$
with $N$ vertices and
$$
\mbox{\rm vol}_{n}(B_{2}^{n}\triangle P)
\leq c\ \mbox{\rm vol}_{n}(B_{2}^{n})N^{-\frac{2}{n-1}}
$$
where $B_{2}^{n}$ denotes the Euclidean ball of dimension $n$.
We compare it to earlier known results which had restrictions on the
approximating polytope.
Thursday, September 28, 2006
3:30-4:20 p.m.
105 General Classroom Building
Refreshments will be served at 3:00 p.m. in Room 326 Mathematical
Sciences (Math Lounge).
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