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Analysis on Graphs and its Applications Follow-up

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Workshop
26th July 2010 to 30th July 2010

Organisers: BM Brown (Cardiff), P Exner (Czech Academy of Sciences), P Kuchment (Texas A&M) and T Sunada (Meiji)

Supported by the Meiji Institute for Advanced Study of Mathematical Sciences; Meiji University Global Centre of Excellence Programme, National Science Foundation (NSF) and the Doppler Institute for Mathematical Physics and Applied Mathematics, Prague

Workshop Theme

The 2007 programme concentrated on three major intertwined areas: Analysis on Discrete Graphs (also called Discrete Geometric Analysis), Analysis on Fractals and Analysis on Quantum Graphs. Applications to various areas of mathematics, sciences, and engineering (specifically, to chemistry, optics, nano-technology, material science, waveguide theory, etc.) were also thoroughly discussed.

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Since the end of the programme, many advances in these areas have occurred. Token examples could be the recent major progress in understanding of possibilities and limitations of graph modeling of meso-and nano-structures; spectral theory progress on quantum graphs, including for instance better understanding of the nodal structure of eigenfunctions and of structure of spectra of various important graph operators, as well as applications to vacuum energy and Casimir effect; discovering and exploring fruitful relations between the newly developed theory of self-similar groups and analysis on fractals; progress in analysis on covering graphs and in geometric crystallography, as well as in graph-theoretic zeta functions.

The workshop will assemble a diverse group of mathematicians and physicists working or interested in furthering the progress of this fast developing and fascinating inter-disciplinary area.

Keynote speakers:

  • Brian Davies (Kings College London)
  • Daniel Grieser (Carl von Ossietzky Universitat Oldenburg)
  • Graeme Milton (University of Utah)
  • Uzy Smilansky (Weizmann Institute of Science)

 

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