Research outputs per year
Research outputs per year
Accepting PhD Students
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Renormalisation in Dynamical Systems
I am the Associate Head for Research and Innovation and a Principal Lecturer in the School of Mathematics and Physics at the University of Portsmouth in the UK. I am also an Associate Member of the Institute of Cosmology and Gravitation. My main research interests are in nonlinear dynamics.
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 also 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 University of Portsmouth in 2005, and am now a member of the Applied Mathematics Group.
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 Portsmouth Cafe Scientifique.
Roles:
Associate Head of School (Research and Innovation) (2019-date)
Principal Lecturer in Mathematics (2012-date)
REF Unit of Assessment Coordinator, UoA10 Mathematics (2012-date)
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 Portsmouth (2006-2016)
Department Web Manager & Publicity Officer (2005-2016)
Postgraduate Admissions Tutor, Department of Mathematics (2011-2012)
Induction Coordinator, Mathematics, University of Portsmouth (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:
2019-date Associate Head (Research and Innovation), School of Mathematics and Physics, University of Portsmouth, UK.
2012-date Principal Lecturer. Department of Mathematics, University of Portsmouth, UK.
2005-2012 Senior Lecturer. Department of Mathematics, University of Portsmouth, UK.
2001-2005 Scientific Programmer (Permanent Post). School of Mathematics, University of Bristol, UK.
1998-2001 Lectured Mathematical Tripos Part III (Applied). Postdoctoral Research Associate. Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics (DPMMS), University of Cambridge, UK.
1997-1998 Postdoctoral Fellow, Basic Research Institute in the Mathematical Sciences (BRIMS), Hewlett-Packard Laboratories Europe, Bristol, UK.
1995 (Sep-Oct) Visiting Fellow, Santa Fe Institute, New Mexico, USA.
1993-1997 PhD, Mathematics, Renormalisation for Siegel Discs, Loughborough, UK.
1990-1993 BSc, Mathematics and Computation, Loughborough, UK.
1. Universality and Renormalisation in Dynamical Systems, Computer-Assisted Proofs in Banach Spaces.
2. Applied Nonlinear Dynamics, e.g., Cancer Modelling 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 and in collaboration with Andreas Stirnemann. 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.
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This person’s work contributes towards the following SDG(s):
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Andrew Burbanks (Participant)
Activity: Participating in or organising an event types › Participation in workshop, seminar, course
Andrew Burbanks (Member of programme committee)
Activity: Participating in or organising an event types › Participation in workshop, seminar, course
Andrew Burbanks (Participant)
Activity: Participating in or organising an event types › Participation in workshop, seminar, course
Andrew Burbanks (Member)
Activity: Membership types › Membership of committee or panel
Andrew Burbanks (Speaker)
Activity: Talk or presentation types › Invited talk