1024ºË¹¤³§

Summary

I am an Associate Professor (Reader) in Applied Mathematics and the Associate Head for Research and Innovation in the School of Mathematics and Physics at the 1024ºË¹¤³§ in the UK.  I am also an Associate Member of the Institute of Cosmology and Gravitation. My main research interests are in nonlinear dynamics.

Biography

I completed my PhD at the University of Loughborough, after which I went on to work at Hewlett-Packard's research laboratories in Bristol before taking up Postdoctoral research positions in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge and later in the School of Mathematics at the University of Bristol where I gained a permanent post as Scientific Programmer.

I gave a course of lectures in Part III of the University of Cambridge Mathematics Tripos (Applied) on renormalisation in Dynamical Systems.

I joined the Department of Mathematics at the 1024ºË¹¤³§ in 2005, and am now a member of the Applied Mathematics Group, becoming Principal Lecturer in 2012, Associate Head for Research and Innovation in 2019, and Associate Professor (Reader) in Applied Mathematics in 2023.

I have been involved in several successful projects on the interface between science and public understanding, including the Mathematics Posters on the London Underground project in 2000, with the Isaac Newton Institute for Mathematical Sciences in Cambridge, and the Dynamics of Spin exhibit at the Royal Society Summer Science Exhibition in London in 2007 and at Techfest (Asia's largest Science and Technology festival) held in Mumbai in 2008. I also co-founded and chaired the 1024ºË¹¤³§ Cafe Scientifique.

Roles

• Associate Professor (Reader) in Applied Mathematics (2023-date)
• Departmental Director of Postgraduate Research (2011-2012, 2021-2023)
• Associate Head of School (Research and Innovation) (2019-date)
• REF Unit of Assessment Coordinator, UoA10 Mathematics (2012-date)
• Principal Lecturer in Mathematics (2012-2023)
• Isaac Newton Institute, Cambridge, Correspondent (2006-date)
  International Centre for Mathematical Sciences, Edinburgh, Correspondent (2018-date)
• Associate Member, Institute of Cosmology and Gravitation (2005-date)
• Research Coordinator, Department of Mathematics (2011-2019)
• Co-founder & Chair, Café Scientifique 1024ºË¹¤³§ (2006-2016)
• Department Web Manager & Publicity Officer (2005-2016)
• Induction Coordinator, Mathematics, 1024ºË¹¤³§ (2009-2011)
• Annual Festival of Maths & Art Team (2005-2010)

Professional Memberships

• 1998-date London Mathematical Society (LMS)
• 2001-date Free Software Foundation
• 2000-2003 SIAM (Society for Industrial and Applied Mathematics)
• 1993-2000 Graduate Member of the IMA (Winner: Loughborough IMA Prize 1993)

Recent Career History

• 2005-date School of Mathematics and Physics, 1024ºË¹¤³§, UK
  2023-date Associate Professor (Reader) in Applied Mathematics
  2019-date Associate Head (Research and Innovation)
  2012-2023 Principal Lecturer
  2005-2012 Senior Lecturer
• 2001-2005 School of Mathematics, University of Bristol, UK.
  Scientific Programmer (Permanent Post)
  Postdoctoral Fellow
• 1998-2001 Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics (DPMMS), University of Cambridge, UK
  Lectured Mathematical Tripos Part III (Applied)
  Postdoctoral Research Associate
• 1997-1998 Basic Research Institute in the Mathematical Sciences (BRIMS), Hewlett-Packard Laboratories Europe, Bristol, UK
  Postdoctoral Fellow
• 1995 (Sep-Oct) Santa Fe Institute, New Mexico, USA
  Visiting Fellow
• 1990-1997 Department of Mathematical Sciences, University of Loughborough, UK
  1993-1997 PhD, Mathematics, Renormalisation for Siegel Discs
  1990-1993 BSc, Mathematics and Computation

Research interests

1. Universality and Renormalisation in Dynamical Systems, Computer-Assisted Proofs in Banach Spaces.

2. Applied Nonlinear Dynamics including Mathematical Oncology (via ODE and DDE models).

3. Nonlinear dynamics in systems of coupled units; localisation, ratchets, collective phenomena, transport in phase space.

In my PhD, I worked under the supervision of Andrew Osbaldestin (Loughborough) and in collaboration with Andreas Stirnemann (Exeter, Edinburgh). I used computer-assisted techniques to explain the universality observed in the breakup of quasiperiodicity (conjugacy to rigid rotation) on the boundary of Siegel discs in complex maps - a prototypical KAM-type scenario.  For golden mean rotation number, I used bounds on the fixed point of the corresponding (Fibonacci-type) renormalisation operator to verify the necklace hypotheses of Stirnemann and thereby to give a rigorous proof of conjectures of Widom explaining the universality observed by Manton and Nauenberg.

While at the University of Cambridge I worked with Colin Sparrow (Cambridge), Jeremy Gunawardena (BRIMS, Hewlett-Packard Laboratories) and Roger Nussbaum (Rutgers) on the dynamics of nonexpansive maps, with applications to discrete event systems.

At the University of Bristol I worked with Stephen Wiggins and Holger Waalkens (Bristol), David Farrelly (Utah State), and others, on transport phenomena in Hamiltonian systems, with applications to problems in Physics, Chemistry, and Celestial Mechanics.

More recently, I have continued my work on renormalisation in dynamical systems (with a focus on coupled systems) and have worked with Marianna Cerasuolo (1024ºË¹¤³§) on mathematical models of prostate cancer.