Mathematics

Andrew Burbanks

Dr Andrew Burbanks

Senior Lecturer

Mathematics

Department of Mathematics, University of Portsmouth, Lion Gate Building, Lion Terrace, Portsmouth PO1 3HF

andrew.burbanks@port.ac.uk

http://userweb.port.ac.uk/~burbana/

Profile

Dr Andrew Burbanks is a Senior Lecturer in Mathematics and an Associate Member of the Institute of Cosmology and Gravitation at the University of Portsmouth in the UK. His main research interests are in nonlinear dynamics and the visualisation of mathematical structures.

Dr Burbanks completed his PhD at the University of Loughborough, after which he 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 at the University of Cambridge and later in the School of Mathematics at the University of Bristol.

Dr Burbanks has 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. He is also co-founder and chair of the Portsmouth Cafe Scientifique.

Additional roles include:

  • Isaac Newton Institute, Cambridge; Research Correspondent
  • Department Web Manager & Publicity Officer
  • Co-founder & Chair, Café Scientifique Portsmouth
  • Section Chief Editor, DSWeb Picture Gallery
  • Annual Festival of Maths & Art Team

Research Focus

  • Dynamical Systems
  • Dynamically Evolving Networks
  • Visualisation of Mathematics Structures

Recent Publications

  • Formula to compute the microcanonical volume of reactive initial conditions in transition state theory.
    Waalkens H, Burbanks A, Wiggins S.
    J. Phys. A.: Math. Gen. 38, L759-L768, 2005.
  • Efficient procedure to compute the microcanonical volume of initial conditions that lead to escape trajectories from a multi-dimensional potential well.
    Waalkens H, Burbanks A, Wiggins S.
    Phys. Rev. Lett., 95, 084301, 2005.
  • Escape from Planetary Neighbourhoods.
    Waalkens H, Burbanks A, Wiggins S.
    Mon. Not. Royal Astron. Soc., 361, 763-775, 2005.
  • Phase Space Conduits for Reaction in Multi-Dimensional Systems.
    Waalkens H, Burbanks A, Wiggins S.
    J. Chem. Phys., 121 (13), 6207—6225, 2004.
  • A procedure to detect a new type of chaotic saddle; application to 3-d Hill's problem.
    Waalkens H, Burbanks A, Wiggins S.
    J. Phys. A., 37 (24), L257—L265, 2004.
  • Dynamics of capture in the restricted three-body problem.
    Astakhov S, Burbanks A, Farrelly D, Wiggins S.
    Astronomical Society of the Pacific “Order & Chaos in Stellar & Planetary Systems”, CS-316, 2004.
  • Chaos-Assisted Capture of Irregular Moons.
    Astakhov S, Burbanks A, Farrelly D, Wiggins S.
    Nature, 423, 264—267, 2003.
  • Extension of order-preserving maps on a cone.
    Burbanks A, Nussbaum R, Sparrow C.
    Proc. Royal Soc. Edinburgh, 133A, 35—59, 2003.
  • Remarks on continuous extension of order-preserving homogeneous maps.
    Burbanks A, Nussbaum R, Sparrow C.
    Kybernetica, 39(2), 205—215, 2003.
  • Continuous extension of order-preserving homogeneous maps.
    Burbanks A, Sparrow C.
    Proc. IFAC Symposium, August 2001, Prague, Czech Republic. Max-Plus Algebras.
  • Monotone homogeneous functions admit continuous extension.
    Burbanks A, Sparrow C.
    Statistical Laboratory, University of Cambridge, Research Report 1999-13.
  • Extracting beauty from Chaos.
    Burbanks A.
    Public Awareness & Schools Support for Maths (PASS Maths/+plus), 9, Sep 1999.
  • Rigorous Bounds on the Hausdorff Dimension of Siegel discs.
    Burbanks A, Osbaldestin A, Stirnemann A.
    Communications in Mathematical Physics, 199(2), 417—439, 1998.
  • Fractal Dimension of Siegel Disc Boundaries.
    Burbanks A, Osbaldestin A, Stirnemann A.
    European Journal of Physics B, 4, 263—265, 1998.
  • Renormalization for Siegel Discs.
    Burbanks A.
    Ph.D. Thesis, Loughborough, 1997.
  • Hölder Continuous Siegel Disc Boundary Curves.
    Burbanks A, Stirnemann A.
    Nonlinearity, 8 (6), 901—920, 1995.

Recent Seminars

Recent International Seminars

  • Apr 2005 - Centres Recherches Mathematiques, Montreal, Quebec, Canada.
  • Sep 2004 - Department of Physics, Nara Women's University, Nara, Japan.
  • Sep 2004 - Nonlinear Science Laboratory, Kobe University, Kobe, Japan.
  • May 2003 - SIAM Conference: Applications Of Dynamical Systems, Utah, U.S.A.
  • Jun 2002 - Libration Point Orbits and Applications, Girona, Catalonia, Spain.
  • May 2002 - 4th International Conference on Dyn. Sys. & Diff. Eqs., N.C., U.S.A.
  • May 2002 - Centre for Nonlinear Sciences, Georgia Tech, G.A., U.S.A.
  • Aug 2001 - IFAC/IEEE System Structure & Control, Prague, Czech Republic.
  • Jul 2000 - European network ALAPEDES, Haus Rissen, Hamburg, Germany.
  • Jun 1997 - A.M.'97 Art & Mathematics Conference, Albany, New York, U.S.A.
  • Nov 1995 - Santa Fe Institute, Santa Fe, New Mexico, U.S.A.

Recent Invited National Seminars

  • July 2007 - Royal Society Summer Science Exhibition. The Dynamics of Spin.
  • 19th May 2007 - Sixth Institute of Mathematics and its Applications (IMA)Younger Mathematicians Conference, LMS, London.
  • May 2006 - Engineering Mathematics, University of Bristol.
  • May 2006 - Computational Science & Applications, University of Portsmouth.
  • Apr 2006 - Department of Computer Science, University of Aberystwyth.
  • Nov 2005 - Institute of Cosmology and Gravitation, University of Portsmouth.
  • May 2005 - East Midlands Mathematical Physics meeting, University of Nottingham.
  • Mar 2005 - Qualitative Numerical Analysis of High-Dim. Nonlinear Systems, Engineering Mathematics, University of Bristol.
  • Nov-Dec 2003 - Working dynamics seminars, School of Mathematics, University of Bristol.
  • Apr 2002 - Department of Engineering Mathematics, University of Bristol.
  • Mar 2002 - Semi-classical/quantum multi-body systems, Mathematics, Warwick.
  • Sep 2001 - London Mathematical Society Regional Meeting, Bristol.
  • Jun 2001 - 52nd meeting of Colston Research Society, Bristol.
  • Jul 2000 - Non-expanding maps, Hewlett-Packard Laboratories, Bristol.
  • Jun 2000 - Nonlinear Day, D.A.M.T.P., University of Cambridge.
  • Sep 1999 - Non-expansive maps & fractals, Hewlett-Packard Laboratories, Bristol.
  • Feb 1999 - Applied Math. & Numerical Analysis, University of Bristol.
  • Oct 1998 - Nonlinear Centre, D.A.M.T.P., University of Cambridge.
  • Feb 1998 - B.R.I.M.S., Hewlett-Packard Laboratories, Bristol.
  • Apr 1997 - E.P.S.R.C. Nonlinear Spring School, U. Loughborough. (Winner: James Yorke Poster Prize.)

Expository Seminars

  • Sep 2004 - (Visualization) Nonlinear Science Lab., Kobe University, Kobe, Japan.
  • Oct 2001 - (Logic) Engineering Mathematics, University of Bristol.
  • May 2000 - (Complex systems) Nonlinear & Complex Systems, U. Loughborough.
  • Nov 1999 - (Logic) D.P.M.M.S., University of Cambridge.
  • Oct 1999 - (Logic) Trinity College Maths Society, University of Cambridge.
  • Jan 1996 - (Complex systems) Mathematical Sciences, University of Loughborough.
  • Dec 1994 - (Complex systems) Mathematical Sciences, University of Loughborough.
  • Nov 1995 - (Dynamical systems) Santa Fe Institute, New Mexico, U.S.A.

Recent Conference Participation

  • 9-13/7/2007 - Dynamics Days Europe, University of Loughborough, UK.
  • 8-10/11/2006 - Annual Festival of Art and Mathematics 2006, University of Portsmouth.
  • 4-10/8/2006 - Bridges Mathematics and Art Conference, London Knowledge Lab.
  • /7/2006 - Summer School on Complex Networks: Analysis, Control, and Applications. Department of Engineering Mathematics, University of Bristol.
  • /10/2005 - Annual Festival of Art and Mathematics 2005, University of Portsmouth.
  • Apr 2005 - Centres Recherches Mathematiques, Montreal, Quebec, Canada.
  • May 2003 - SIAM Conference: Applications Of Dynamical Systems, Utah, U.S.A.
  • Jun 2002 - Libration Point Orbits and Applications, Girona, Catalonia, Spain.
  • May 2002 - 4th International Conference on Dyn. Sys. & Diff. Eqs., N.C., U.S.A.
  • Aug 2001 - IFAC/IEEE System Structure & Control, Prague, Czech Republic.
  • Jul 2000 - European network ALAPEDES, Haus Rissen, Hamburg, Germany.
  • Jun 1997 - A.M.'97 Art & Mathematics Conference, Albany, New York, U.S.A.

Recent Conference Organisation

  • 8-10/11/2006 - Annual Festival of Art and Mathematics 2006, University of Portsmouth.
  • 2006--date - Co-Founder, co-organiser, and chair, Cafe Scientifique, Portsmouth.
  • /10/2005 - Annual Festival of Art and Mathematics 2005, University of Portsmouth

Professional Memberships

Recent Career History

  • 2005-date. 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, DPMMS, University of Cambridge, UK.
  • 1997-1998. BRIMS, Hewlett-Packard Laboratories Europe, Bristol, UK.

Grants Obtained

  • 2003 Leverhulme Trust, Artist in Residence Programme. Funding for Simon Thomas (RCA), sculptor, to be Artist in Residence in the Department of Mathematics at the University of Bristol.

Recent Teaching Activities

  • 2006/7-2007/8 - Unit MTH316 Financial Derivative Pricing 1.
  • 2006/7-2007/8 - Unit MTH317 Financial Derivative Pricing 2.
  • 2005/6-2007/8 - Unit MTH301 Non-Linear Dynamical Systems.
  • 2006/7-2007/8 - Unit MTH399 Advanced Mathematical Programming.
  • 2006/7-2007/8 - Unit PRO302 Final Year Project (Supervisions).
  • 2007/8 - Unit APM204 Introduction to Investments.
  • 2007/8 - Unit MTH200 Mathematics Graduates and Employment (Tutor).
  • 2005/6-2007/8 - Unit MTH150 Elementary Calculus (Tutor).
  • 2005/6-2007/8 - Unit MTH155 Further Calculus and Linear Algebra (Tutor).
  • 2005/6-2007/8 Maths Café (Drop-in Centre).
  • 2006/7 - Unit CMP305 Introduction to Programming with C++.
  • 2000/1-2000/2 - Renormalisation for Dynamical Systems, Mathematical Tripos Part III, DAMTP, University of Cambridge, U.K.

Mathematical and Related Graphics & Design

Outline

Exhibits, Installations & Appearances

  1. Royal Society, Summer Science Exhibition, 2007. The Dynamics of Spin. July 2007.
  2. Rothamsted Research Institute, Open Weekend
    Fractal exhibition [Image contribution], Oct 2006.
  3. Dr. Who, BBC Television [Set-dressing]
    Mathematical Posters on the London Undeground, 2006.
  4. Mathematical Artwork [Exhibit]
    Annual Festival of Mathematics & Art 2005, University of Portsmouth, UK, 2005.
  5. BigBang [Permanent Installation]
    Anglesea Building, Faculty of Technology, University of Portsmouth, UK, 2005.
  6. Maths on the Boston Subway [Boston Subway; Poster Series]
    Clay Mathematics Institute (adapted from London Underground series), Boston, USA, 2004.
  7. Reprint of London Underground Posters [Poster Distribution]
    Mathematical Association, USA, 2003.
  8. Artist in Residence [Permanent Installation]
    with Simon Thomas (Sculptor)
    Leverhulme Trust Artist in Residence Programme, School of Mathematics, University of Bristol, UK, 2003.
  9. Reprint of London Underground Posters [Poster Distribution]
    World Scientific Press, 2002.
  10. Maths Goes Underground [Exhibit]
    BA Creating Sparks Festival,
    Royal College of Art, London, UK, 2000.
  11. Dawson's Creek, Sony Pictures Television, USA [Set Dressing]
    Maths Goes Underground Poster Series, 2002.
  12. Mathematics Posters on the Underground [London Underground; Advertisments]
    Series of 12 posters with Isaac Newton Institute, Cambridge, UK, for World Mathematical Year 2000.
    London Underground, London, UK, 2000.
    Winner: HEIST Education Marketing Award (Merit).
  13. Technological Artwork [Permanent Installation]
    Directrix Inc., USA, 1999.
  14. Order in Space [Web Site & Exhibit]
    with Simon Thomas (Sculptor)
    Hewlett-Packard Laboratories, Bristol, UK, 1998.
  15. Lyapunov Space [Permanent Installation; Glass Panel Print]
    Staff Coffee Area, Building 3 Project,
    Hewlett-Packard Laboratories, Bristol, UK, 1997.

Journal & Book Contributions

  1. Digital Media: An Introduction [Book; Image Contributions]
    by Richard Lewis & James Luciana, Prentice Hall, ISBN10: 013-087-390-X, 2005.
  2. Underground to Everywhere [Image Contribution]
    London's Underground Railway in the Life of the Capital, by Stephen Halliday, Sutton Publishing, ISBN10: 075-093-843-9, 2004.
  3. Mathematics & Programming with Mathematica [Book Cover]
    by Nikos Karampetakis et al., Thessalonika, ISBN10: 960-431-897-7, 2004.
  4. Nature [Image Contribution, Contents Section]
    Nature, Volume 423 Number 6937 pp207-365, Nature Publishing Group, 2003.
  5. re:search [Cover, and several image contributions]
    re:search, University of Bristol research magazine, Issue 4, July 2003.
  6. Lyapunov Image [Book Cover]
    for The Gospel of Christian Atheism by Thomas Altizer, Davies Group Publishers, Paperback Edition, (Hardback ISBN10: 188-857-065-2), 2003.
  7. The Story of Mathematics [Book; Image Contributions]
    by Richard Mankiewicz, Princeton University Press, ISBN10: 069-108-808-X, 2001.
  8. Probability & Random Processes [Book Cover; Design Assistance] and One Thousand Exercises in Probability [Book Cover; Design Assistance]
    by Geoffrey Grimmett & David Stirzaker, Oxford University Press, ISBN10: 019-857-222-0 & 019-857-221-2, 2001.
  9. Mathematics Galore! [Image Contribution]
    Masterclasses, Workshops, and Team Projects in Mathematics and Its Applications, by Christopher Budd & Christopher Sangwin, Oxford University Press, ISBN10: 019-850-770-, 2001.

Annual Reports, Prospectuses, Logotypes, Booklets

  1. Mathematics at Bristol [Prospectus Cover]
    School of Mathematics, University of Bristol, UK, 2002.
  2. Maths Goes Underground [Booklet]
    with Isaac Newton Institute, Cambridge, UK, 2002.
  3. Maths Counts - in the Support of Science & Technology [Report Cover]
    Isaac Newton Institute, Cambridge, UK, 2000-2001.
  4. Isaac Newton Institute Annual Report [Cover]
    University of Cambridge, UK, 1999-2000.
  5. IT Skills Guide, University Prospectus, Department Brochure [Covers]
    University of Loughborough, UK, 1995.
  6. Nonlinear & Complex Systems Group [Logotype]
    Department of Mathematics, University of Loughborough, UK, 1994.

Event Advertisments, Posters, Flyers

  1. Café Scientifique Portsmouth [Posters, Flyers]
    University of Portsmouth & Portsmouth City Council, UK, 2006.
  2. Computational Science and Applications Interdisciplinary Research Seminar Series [Posters, Flyers]
    Department of Mathematics, University of Portsmouth, UK, 2006.
  3. Student-led & ICG/Maths Lecture Series [Posters, Flyers]
    Department of Mathematics, University of Portsmouth, UK, 2005.
  4. Postgraduate Mathematics & Bristol [Recruitment Posters]
    Including overseas recruitment poster. School of Mathematics, University of Bristol, UK, 2004.
  5. SPA27 Stochastic Processes & Applications [Poster Advertisment]
    Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, UK, 2001.

Web Sites & Web Contributions

  1. Department of Mathematics, University of Portsmouth [Web Site]
    2005-date.
  2. DSWeb Picture Gallery [Section Chief Editor]
    Picture Gallery, DSWeb, 2005-date.
  3. Simon Thomas, Sculptor [Web Site Contribution]
    Spike Island Sculpture, Bristol, UK, 2004.
  4. Laboratory for Advanced Computation in Mathematical Sciences [Web Site]
    School of Mathematics, University of Bristol, UK, 2002-2005.
  5. Web Site of Author Fritjof Capra [Image Contribution]
    Fritjof Capra, Berkeley, California, USA, 2001.
  6. Café Etalon [Web Site; Image Contribution]
    Photonics Discussion Group, 1999.
  7. Florida Community College [Web Site; Image Contribution]
    Jacksonville, USA, 1999.
  8. Statistical Laboratory [Web Site]
    Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, UK, 1999-2001.
  9. Order In Space [Web Site]
    Hewlett-Packard Laboratories, Bristol, UK, 1997-1998.
  10. Gallery of Mathematical Images [Web Site]
    with Keith Beardmore, Department of Mathematics, University of Loughborough, UK, 1996.
    Winner: Dr. Matrix Science Web Site Award.
  11. Department of Mathematics [Web Site]
    University of Loughborough, UK, 1995-1997.

Theatrical Collaboration

  1. Arcadia, by Tom Stoppard [Informal Maths Seminars for the Cast]
    (with Prof. Jon Keating, School of Mathematics, University of Bristol).
    Bristol Old Vic Theatre, October 2004.

Other Commissions & Works

  1. Mathematics at Bristol & At Bristol [DVD Covers, Inserts, DVD Print]
    School of Mathematics, University of Bristol, UK, 2004.
  2. Simon Thomas, Sculptor [Portfolio CD & CD Cover]
    Spike Island Sculpture, Bristol, UK, 2004.
  3. Millennium Maths Project - Motivate [Video Sleeve; Contribution]
    Department of Applied Maths & Theoretical Physics, University of Cambridge, UK, 2000.
  4. Quaternionic Landscape [Cover Image; Credit-Card CD]
    Ultrium Marketing Group,
    Hewlett-Packard Laboratories, Bristol, UK, 1999.
  5. Welcome to BRIMS; Building 3 [Poster Panel]
    BRIMS, Hewlett-Packard Laboratories, Bristol, UK, 1998.
  6. Stretching a Point [Photographic Composite]
    with Simon Thomas (Sculptor), Bristol, UK, 1997.