Alex Clark

Professor and Head of Department

Office: College House 002

Tel: +44 (0)116 252 5670

Email: Alex.Clark@le.ac.uk

 

Publications

Preprints

View a complete list of publications

Research

My research interests are in dynamical systems, foliations, topology and their interactions.

I'm PI of this Leicester based international network with nodes in Lyon, Nice, Delft, Krakow and New York. The research focus of the network is the topological spectrum of structures related to quasicrystals.

Recent research summary

  • Minimal Sets and Attractors of Foliations and Dynamical Systems

Minimal sets and attractors often reflect the limiting behaviour of the systems in which they occur. In the recent work New exotic minimal sets from pseudo-suspensions of Cantor systems we discover that minimal sets can have unexpectedly complex behaviour by exhibiting the first examples of  hereditarily indecomposable minimal sets of smooth systems that occur with positive entropy. Also, in the paper A compact minimal space  Y such that its square  Y ×Y is not minimal we present the first example of a compact metric space Y that admits a minimal homeomorphism but is such that Y x Y admits no minimal homeomorphism.

  • Tiling Spaces

The geometry and rates and patterns of recurrence of aperiodic tilings, such as the Penrose tiling,  can be studied and better understood by examination of dynamical systems on related topological spaces known as tiling spaces. The dynamics of the tiling spaces have important links with the diffractive properties of quasicrystals with analogous structure. In the paper Small cocycles, fine torus fibrations, and a Z2 subshift with neither we find the first examples of tiling spaces that have no small cocycles. This has the important consequence that the formalism of Bratteli diagrams cannot be generally applied in higher dimensional dynamical systems. In The homology core and invariant measures we use positive cones in homology to find new topological  invariants for spaces that generalise the classical tiling spaces and relate this invariant to the structure of the space of invariant measures for the associated dynamical system.

Conferences and seminars

Recent grants

Supervision

  • Ahmed Al-Hindawe
  • Petra Staynova
  • Dina Abuzaid; graduated 2016. Lecturer at King Abdulaziz University
  • Dan Rust (contains a link to download Grout), graduated 2016. Currently post-doctoral at the University of Bielefeld
  • James Walton ; Blog explaining thesis (first three years supervised by John Hunton). Currently at Durham University
  • Sheila McCann, graduated August 2013. Currently an RA in Leicester

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Contact details

Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 252 3917
Fax: +44 (0)116 252 3915

Campus Based Courses

Undergraduate: mathsug@le.ac.uk
Postgraduate Taught: mathspg@le.ac.uk

Postgraduate Research: pgrmaths@le.ac.uk

Distance Learning Course  

Actuarial Science:

sep-dl@le.ac.uk  

 

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