Alex Clark

  • Tuesday 16 May 2017
  • 6.00pm-7.00pm
  • Centre for Medicine, Lecture Theatre 1

When shape matters: from Topology to Tilings

Topology provides a way to study geometric properties in an abstract way. It is perhaps surprising then that topology can be used to describe and in some cases even measure the behaviour of dynamical systems, which are mathematical models that describe the way a wide variety of types of systems evolve over time.

We will begin by considering some general constructions illustrating the unusual and unexpected topology that we have discovered that can arise in dynamics. Afterwards, we will consider how aperiodic tilings and their associated quasicrystals can be better understood with the aid of topology. This leads to the surprising result that topology can be used to detect which patterns of quasicrystals would maintain their key properties after small deformations.

Professor Alex Clark, Professor of Mathematics

Alex 200x266.jpgAlex Clark was born in Birmingham, Alabama USA and studied at Indian Springs school, leaving one year early to attend Harvard. While in high school he studied Latin and taught himself Ancient Greek, earning a high mark on the National Greek exam. At Harvard he studied Linguistics with the allied field of Mathematics, which included the ancient language of Hittite.

Clark then decided to focus on mathematics and attended Auburn University where he earned his PhD under the supervision of Krystyna Kuperberg in 1998. Upon graduation he took a position as Assistant Professor at the University of North Texas, where he was promoted to Associate Professor with tenure in 2005. In 2008 he took up a Lectureship at the University of Leicester where he was promoted to Reader in 2010. In 2015 Clark was promoted to Professor. In August 2016 Clark assumed the role of Head of Department of Mathematics.

Clark’s research focusses on topology and its interaction with dynamical systems, exploring the unusual structure that limit sets of dynamical systems can have. One particularly interesting side of his research explores the structure of aperiodic tilings and the interpretation of these as dynamical systems. His research has found ways to use topology to study the diffraction spectrum of quasicrystals with patterns that match those of an associated aperiodic tiling.

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