School Seminars and Colloquia

The Knaster problem and related problems from Analysis and Combinatorics

Colloquium

by Professor Boris Kashin


Institution: Steklov Mathematical Institute, Moscow
Date: Wed 3rd November 2004
Time: 11:00 AM
Location: Russell Love Theatre, Richard Berry Building, The University of Melbourne

Abstract: In 1947 B. Knaster posed the following problem: Given a
continuous real function F on the Euclidean sphere S^{n-1} and a
configuration of n points q(1), ..., q(n) in S^{n-1}, is there a rotation
U from SO(n) such that F(Uq(1))=F(Uq(2))=...=F(Uq(n))?

A negative answer to this problem for large enough n was published by B.
Kashin and S. Szarek in 2003. The construction of the counterexample is
based on some geometrical properties of multidimensional cubes and related
to other results from Analysis, Combinatorics and Control theory. In the
talk this connection and the solution of the Knaster problem will be
discussed.

For More Information: Paul Norbury tel. 8344-9711 email p.norbury@ms.unimelb.edu.au

Colloquium Website