John Hunton's WebPage
101 College House
University of Leicester
Telephone: ++44 (0)116 252 5354
Email: jrh7 "at" mcs.le.ac.uk
My main research interests lie at the interface of Algebraic Topology, Dynamical Systems and Noncommutative Geoemtry, particularly in the way they interact in the study of Aperiodically Ordered Patterns and Tilings. See here for a short introduction to the ideas of Aperiodic Order.
A powerful tool used to study the geometry of aperiodic patterns is a method of passing from a given pattern to a certain associated moduli space equipped with a dynamical action of one of the Euclidean groups or their subgroups. This setup is then amenable to study from both topological and dynamical perspectives, but in turn can also be used as an important class of examples of dynamical systems: for example, in recent work with Alex Clark we showed a large class of chaotic attracters were in fact just spaces of aperiodic tilings.
I also have continuing interests in classical algebraic topology, for example in the modeling of infinite loop spaces and their applications, particularly to representation theory, group cohomology and unstable Adams spectral sequences. More details can be found here. See also Research papers listed by topics.
With John Greenlees, Sarah Whitehouse (Sheffield) and Nige Ray (Manchester) I run the LMS funded Scheme 3 Transpennine Topology Triangle, and with collaborators in Leicester, especially Clark, Neumann, Snashall and Schroll, we usually have running seminars on aspects of the topology, dynamics and algebra of aperiodic patterns.
In the academic year 2012/13, I have been continuing to teach the analysis stream, and other topics, for our September 2011 intake cohort.
Over the years I have been lucky enough to work with some very singular and inspiring PhD students and research assistants, including current and recent individuals Claire Irving, Marcello Felisatti, David Fletcher, Andrew Peden and Jamie Walton.
Over the last few years with colleagues I have developed and become a keen advocate of a problem based learning component to the undergraduate maths degrees in Leicester. This is a handcrafted "UK" version of the american Moore Method approach, and, not only is it highly popular, it makes a significant contribution to the development of students' abilities to read, write and think about mathematics in a serious and professional manner. If you're interested to know more, then do get in touch.
Since 1999 I have served on the EPSRC College and was a member of the EPSRC Strategic Advisory Team for the Mathematical Sciences 2010-2013.
I am a member of the Scientific Steering Committee of the British Mathematical Colloquia, and was chair of the 2011 BMC, held in Leicester. See here to find out what exciting things you missed if you didn't come to it.
In the current climate it seems crucial that mathematics, in particular pure maths, is visible and works to explain its importance to society at large. Our exhibition How do shapes fill space? was selected by the Royal Society for its Summer Science Exhibition in 2009, has subsequently toured a number of science festivals and has be made into a sequence of Masterclasses at the Royal Institution.
Here are some contributions on numbers with interesting geometric or topological properties I have made to Brady Haran's Numberphile series on YouTube: look at Five for some chat on tiling problems and quasicrystals, and see Three for some shots of Borromean Rings.
The process of making mathematics tangible to the non-mathematician has also led me to both train as a silversmith (see the Borromean Rings video for an example) and self-train to work with real tiles, not just pencil and paper ones; here is a part of the aperiodic Ammann-Beenker tiling (a irrational slice of a regular tessellation of euclidean 4-space by cubes) progressing up a kitchen wall in Nottiinghamshire. A number of my students have also become interested in the process of physically creating representations of mathematical objects: see here for Claire Irving's knitting and crochet patterns for projective spaces, which made the front cover of the Math Gazette.