Steve Vickers
Dr Steve Vickers
School of Computer Science

Research
Since October 2018 I have retired, so that I can focus on my research. I still supervise PhD students, and I am a member of the Theoretical Computer Science research group.
My particular interest is in toposes as generalized spaces, with the connection between logic (specifically, geometric logic) and topology. These are areas of mathematics that have connections with computer science, although my work in them is often purely mathematical. Over 201718 I formalized an approach to topos theory using Joyal's Arithmetic Universes (AUs) as a substitute for Grothendieck toposes, potentially implementable on computers, and showed how to use it to obtain constructive, basefree results for toposes. My current work is on developing the techniques of this approach and exploring the extent to which it can capture Grothendieck's original applications of topos theory.
On the research page you can also find opportunities for PhD study with me. If you are interested in doing that, look at my Research page and feel free to contact me.
Before I joined Birmingham I was at the Department of Pure Maths at the Open University, and before that I was at the Department of Computing at Imperial College, where I worked in the Theory and Formal Methods group.
You can download many of my papers and talks, and also theses of some of my former PhD students.
For three years from September 2009 I was principal investigator on an EPSRCfunded project Applications of geometric logic to topos approaches to quantum theory, an interdisciplinary project to look at the connections between geometric logic and some new topos approaches to quantum physics. This brought out the importance of bundles as fibrewise topology (an example of Grothendieck's relativization techniques).
Teaching
I have taught a variety of Computer Science topics, including Java programming, reasoning about programs (see the book "Reasoned Programming"), Introduction to Computer Science (slogan: How programs work), and Introduction to Maths for Computer Science (a catch up module for students without previous maths qualifications).
You might be interested in some of my old teaching material 
 My turtle graphics applet from when I taught Software Workshop 1. (Warning  This applet doesn't run so easily on recent versions of Java.)
 Quantum Computing and Cryptography.
 An advanced course on Quantum Topos Theory from the 2010 Midland Graduate School in the Foundations of Computer Science.
 Project orientation lecture slides on "Writing good dissertations".
Previous lives
My PhD (at Leeds) was in algebra under the supervision of Alfred Goldie, and my thesis was "Universal Strongly Regular Rings" (1979).
After that I was a computer programmer for several years. I wrote the ROM and user manuals for two Sinclair computers, the ZX81 and the ZX Spectrum. Then with Richard Altwasser I founded Jupiter Cantab Ltd, which produced the Forthbased Jupiter Ace microcomputer. You might be amused by this video of Spectrums playing part of a Mahler symphony.