## Welcome!

Hello, I'm Kevin Houston, a mathematician in the School of Mathematics at the University of Leeds.

## Research

My research has traditionally been in Singularity Theory, a long and venerable subject dating back to Newton. Recently I have been working in Discrete Differential Geometry, in particular recent ideas surrounding generalizations of the discrete Laplacian.

My first paper in this area is on **compressed manifold modes** (CMMs). The Laplace-Beltrami operator on a manifold gives eigenfunctions that are non-zero on a dense subset of the manifold. In certain situations, functions that are zero on most of the manifold but are non-zero on important features are useful. This is what CMMs give us, see the figure on the right for example. In addition to giving a natural ordering of the modes and making some other practical observations, I propose an algorithm that requires on average 47% fewer iterations than the algorithm proposed by Neumann et al who were following in the footsteps of Ozolins et al.
See my publications for more information.

If you fancy doing a PhD in this area, then please contact me: k.houston(at)leeds.ac.uk

## Mathematical Thinking

My main teaching interest is encouraging (read forcing) students to think, hence the title of my best-selling book, *How To Think Like a Mathematician*.
You might be interested in this taster for it: a free booklet called *10 Ways To Think Like a Mathematician*.