University of Cambridge > > Isaac Newton Institute Seminar Series > Polarisation problems

Polarisation problems

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Mustapha Amrani.

Discrete Analysis

Let $u_1, u_2, ..., u_n$ be unit vectors in a Hilbert space $H$. The polarisation problem states that there is another unit vector $v$ in $H$, which is sufficiently far from the orthogonal complements of the given vectors in the sense that $prod |(u_i, v)| geq n$. The strong polarisation problem asserts that there is choice of $v$ for which $ um 1/ (u_i, v)2 leq n^2$ holds. These follow from the complex plank problem if $H$ is a complex Hilbert space, but for real Hilbert spaces the general conjectures are still open. We prove special cases by transforming the statements to geometric forms and introducing inverse eigenvectors of positive semi-definite matrices.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2022, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity