My Research

I am a Lecturer in the Department of Mathematical Sciences at Loughborough University.

If you came here looking for details of my teaching, click on this link.

My research interests lie in the area of nonlinear dynamical systems, in particular, quantum chaology. To get a more refined idea of the work I do, refer to my publications list (below). For a general introduction in simple terms, the surveys written (not by me) here and here are quite illuminating.

(Photographs from my trips to conferences [and others] are now at my photography page.)

My Curriculum Vitæ

An up-to-date Curriculum Vitæ is available.

My Research Papers

To avoid copyright problems the papers available for download are preprints and may differ ever-so-slightly from the published versions. To read the versions as they appeared in press, contact the relevant publisher.

• B. Winn 'Derivative moments for characteristic polynomials from the CUE' >>preprint<<, >>abstract<<, >>wordcloud<<
• P. Exner, P. Kuchment and B. Winn (2010): `On the location of spectral edges in Z-periodic media'. J. Phys. A 43: art. no. 474022. >>PDF<<, >>abstract<<
• G. Berkolaiko and B. Winn (2010) `Relationship between scattering matrices and spectrum of quantum graphs'. Trans. Amer. Math. Soc. 362 6261-6277. >>PDF<<, >>abstract<<
• J. P. Keating, J. Marklof and B. Winn (2010) `Localised eigenfunctions in Šeba billiards.' J. Math. Phys. 51: art. no. 062101. >>PDF<<, >>abstract<<, >>wordcloud<<
• B. Winn (2008) `A conditionally convergent trace formula for quantum graphs'. In Proceedings of the programme Analysis on Graphs and Its Applications, Cambridge, UK, Proc. Symp. Pure. Math. 77 491-501. >>PDF<<, >>abstract<<.
• J.M. Harrison, U. Smilansky and B. Winn (2007): `Quantum graphs where back-scattering is prohibited'. J. Phys. A 40 14181-14193. >>PDF<<, >>abstract<<
• J.M. Harrison, P. Kuchment, A. Sobolev and B. Winn (2007): `On occurrence of spectral edges for periodic operators inside the Brillouin zone'. J. Phys. A 40 7597-7618. >>PDF<<, >>abstract<<
• B. Winn (2006): `On the trace formula for quantum star graphs'. In Proceedings of the Joint Summer Research Conference: Quantum Graphs and Their Applications, Snowbird, UT, AMS Contemporary Mathematics 415 293-307. >>postscript<<, >>abstract<<
• M. Degli Esposti, S. Nonnenmacher and B. Winn (2006): `Quantum variance and ergodicity for the baker's map'. Commun. Math. Phys. 263 325-352. >>PDF<<, >>abstract<<
• M. Degli Esposti and B. Winn (2005): 'The quantum perturbed cat map and symmetry'. J. Phys. A 38 5895-5912. >>PDF<<, >>abstract<<
• M. Degli Esposti, S. O'Keefe and B. Winn (2005): `A semi-classical study of the Casati-Prosen triangle map'. Nonlinearity 18: 1073-1094 >>PDF<<, >>abstract<<
• G. Berkolaiko, J. P. Keating and B. Winn (2004): `No quantum ergodicity for star graphs'. Commun. Math. Phys. 250:259-285 >>PDF<<, >>abstract<<
• G. Berkolaiko, J. P. Keating and B. Winn (2003): `Intermediate wave-function statistics' Phys. Rev. Lett. 91: art. no. 134103 >>PDF<<, >>abstract<<
• J. P. Keating, J. Marklof and B. Winn (2003): `Value distribution of the eigenfunctions and spectral determinants of quantum star graphs' Commun. Math. Phys. 241:421-452 >>PDF<<, >>abstract<<
• B. D. Mestel, A. H. Osbaldestin and B. Winn (2000): `Golden mean renormalisation for the Harper equation: the strong coupling fixed point' J. Math. Phys 41:8304-8330

My Ph.D. Thesis

• "The Laplacian on a graph and quantum chaology" - Abstract and download.

Mathematical Links

• General Mathematical links
  • Eric Weisstein's World of Mathematics was once the primo reference site for mathematics.
  • Wikipedia is now almost as good (and without the blatant plugs for Wolfram Research products.)
  • Wolfram mathematical functions
  • An online version of Abramowitz and Stegun
  • NIST Digital library of mathematical functions
  • The Tricki
  • MathOverflow
  • The online encyclopædia of integer sequences
  • Common errors in Mathematics
  • A mathematical dictionary in some unusual languages.
  • A mathematics FAQ
  • The Mathematics WWW virtual library at Florida State University
  • Mathematics archives
  • Mathematician of the Day
  • The Primes Pages
  • The Number Theory Web
  • Latin Phrases used in mathematics
  • The London Mathematics Society
  • The Millenium Prize Problems - Win a big prize
  • The AMS directory of Mathematics on the Web
• Links more relevant to my research
  • A list of online journals...
  • ...and a reference for all those journal abbreviations
  • The institute of Physics
  • The Quantum Chaos Network
  • (UK mirror of) E-print archive...
  • ...and a much better front end for the mathematics arXiv
  • The mp_arc archive
  • Want to simplify a sum involving factorials, binomial coefficients? I can recomend reading the book 'A=B'
  • Michael Berry's papers
• Journals I read
  • Physical Review E
  • Communications in Mathematical Physics
  • Journal of Physics A
  • Physics Letters A
  • Journal of Functional Analysis
  • Annals of Physics
  • Proceedings of The Royal Society A
  • Nonlinearity
  • Duke Mathematical Journal
  • JSTOR
  • Annales Institut Henri Poincare
  • Annals of Mathematics
  • Physical Review Letters
  • Physica D
  • Antarctica Journal of Mathematics
• Computing
  • Fortran 77 manual
  • NAG Fortran 77 Libraries
  • SLATEC Fortran 77 Libraries
  • Octave manual
  • Gnuplot manual
  • Gnuplot FAQ
  • The POSTSCRIPT blue book - (Warning! This is a link to a large (ironically) .pdf file)
  • The TeX archives
• Other links
  • Mathematics Departments
    • Bristol
    • Bologna
    • Texas A & M University
    • Mathematics departments in the UK
    • Mathematics departments in Italy
    • Mathematics departments around the world
  • Britney Spears' guide to semiconductor physics
  • Abstruse Goose
  • xkcd

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