Isaac Newton Institute for Mathematical Sciences

Quantum Graphs, their Spectra and Applications

April 2nd - 5th 2007

Organisers: B. M. Brown (Cardiff), W. D. Evans ( Cardiff), P. Exner (Czech Academy of Sciences), J. Keating (Bristol) and P. Kuchment (Texas A&M)

This workshop is a part of the long term Isaac Newton Institute program "Analysis on Graphs and its Applications" (AGA), which runs from January 8 through June 29, 2007.

Workshop's Theme

Analysis on graphs and other discrete structures has been developing for quite some time, in particular due to applications to number theory, algebra, probability theory, spectral geometry, as well as to its usefulness in many practical problems. New objects, so called quantum graphs have emerged recently. These are graphs considered as one-dimensional CW-complexes and equipped with differential or pseudo-differential, rather than customary difference operators. This has happened due to numerous new applications arising in several areas of mathematics, sciences, and engineering, e.g. in nanotechnology, microelectronics, quantum chemistry, superconductivity, optics, etc. Such graphs, besides being in many cases useful low-dimensional models of complex systems, are also used as toy models for studying difficult issues such as Anderson localisation and quantum chaos. The methods used or expected to be useful in analysis on quantum graphs come from a very wide range of topics: algebra, combinatorics, PDEs, spectral theory, micro-local and complex analysis, to name a few.

The workshop will assemble a diverse group of mathematicians and physicists working in or interested in entering this fast developing and fascinating area.

Among the invited participants are

  • M. Belishev, Steklov Institute, St. Petersburg, Russia
  • G. Berkolaiko, Texas A&M University, USA
  • R. Carlson, Univ. Colorado, USA
  • Y. Colin de Verdiere, Fourier Institute, France
  • E. B. Davies, King's College, UK
  • S. Fulling, Texas A&M University, USA
  • V. Geyler, Saransk Univ., Russia
  • S. Gnutzmann, Univ. Nottingham, UK
  • J. Harrison, Texas A&M University, USA
  • A. Klein, Univ. California, Irvine, USA
  • E. Korotyaev, Humboldt Univ., Germany
  • V. Kostrykin, Fraunhofer Inst., Aachen, Germany
  • T. Kottos, Wesleyan Univ., USA
  • P. Kurasov, Lund Inst. Techn, Sweden
  • S. Molchanov, Univ. North Carolina, Charlotte, USA
  • S. Nicaise, Univ. Valenciennes, France
  • B. Pavlov, Univ. Auckland, New Zealand
  • O. Penkin, Belgorod Univ., Russia
  • G. Rozenblioum, Chalmers Univ., Sweden
  • Y. Saito, Univ. Alabama, Birmingham, USA
  • R. Schrader, Freie Univ., Germany
  • R. Sims, Univ. California, Davis, USA
  • U. Smilansky, Weizmann Inst., Israel
  • M. Solomyak, Weizmann Inst., Israel
  • G. Tanner, Univ. Nottingham, UK
  • B. Winn, Texas A&M University, USA
Researchers interested in participating in the workshop should submit their application here.
Questions on the scientific content should be directed to P. Kuchment.
A page for the workshop maintained by the Newton Institute can be found here.