Alex Clark

 


 

Professor and  Head of Department Office College House 002

Phone (0116) 252 5670

Alex.Clark_AT_le.ac.uk


Teaching

Autumn 2016

Investigations in Mathematics, Second Year Module

    Spring 2017

    Strange Attraction, Fourth Year Module

    • Ph D Seminar for Current Students

    • Pure Maths Seminar

    Publications

    Research

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

    International Research Network funded by the Leverhulme Trust

    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. For more details, click here.


    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.

    Preprints

    Complete list of publications


    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 Doc at the University of Bielefeld
    • James Walton ; Blog explaining thesis (first 3 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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