AGA
8 January 2007 to 29 June 2007
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. This area, however, has experienced recently a significant boost in terms of new important applications arising, new methods being developed, and new models introduced not studied before. This has happened due to numerous new applications arising in different areas of mathematics, sciences, and engineering. They swipe throughout a wide scientific landscape, which besides the fields already mentioned includes nanotechnology, microelectronics, quantum chemistry, superconductivity, optics, etc. New objects, so called quantum graphs have also emerged. These are graphs considered as one-dimensional CW-complexes and equipped with differential or pseudo-differential, rather than customary difference operators. 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, scattering, and quantum chaos. This has lead to interest in this research by scientists coming from different fields (physics, partial differential equations, algebra, combinatorics, number theory). The methods already used or expected to be useful in analysis on graphs come from a very wide range of topics: algebra, combinatorics, PDEs, spectral theory, micro-local and complex analysis, to name a few.
The program will assemble, essentially for the first time, a diverse group of prominent mathematicians and physicists, as well as young researchers working in or interested in entering this fast developing and fascinating area. The hope is to facilitate the process of communication and cooperation, thereby promoting accelerated progress in this burgeoning new area. Among the particular topics that will be addressed during the program are: Spectral analysis on combinatorial graphs and its applications to number theory, discrete groups, random walks, and other areas; Quantum graph models for wave propagation in thin structures and for quantum and optical switching and computing; Spectral analysis and quantum chaos on quantum graphs; Analysis on fractals.
Click here to download the programme's final scientific report
Title | Year | Programme | |
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On occurrence of spectral edges for periodic operators inside the Brillouin zoneAuthors: Alex Sobolev, Jon Harrison, Peter Kuchment, ET Al |
2006 | AGA | 21 October 2016 |
Modified Krein formula and analytic perturbation procedure for scattering on arbitrary junctionAuthors: Boris Pavlov, A Yafyasov, A Adamyan |
2006 | AGA | 21 October 2016 |
A linear Wegner estimate for alloy type Schrödinger operators on metric graphsAuthors: I Veselic, M Helm |
2006 | AGA | 21 October 2016 |
Spectral asymptotics of percolation Hamiltonians on amenable Cayley graphsAuthors: T Antunovic, I Veselic |
2006 | AGA | 21 October 2016 |
The maximum principle for elliptic inequalities on stratified setsAuthors: Oleg Penkin, SN Oshepkova |
2006 | AGA | 21 October 2016 |
Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over ${\mathbb Z}^d$Authors: Daniel Lenz, I Veselic, Michael Gruber |
2006 | AGA | 21 October 2016 |
Mathematics of thermoacoustic and photoacoustic tomographyAuthors: L Kunyansky, Peter Kuchment |
2006 | AGA | 21 October 2016 |
Inverse problems for quantum treesAuthors: P Kurasov, Sergei Avdonin |
2006 | AGA | 21 October 2016 |
Vacuum energy and repulsive Casimir forces in quantum star graphsAuthors: L Kaplan, Justin Wilson, Stephen Fulling |
2006 | AGA | 21 October 2016 |
An index theory for uniformly locally finite graphsAuthors: Joachim von Below |
2006 | AGA | 21 October 2016 |
The problem of fitting of the zero-range model of the tectonic plate under a localized boundary stressAuthors: Boris Pavlov, L Petrova |
2006 | AGA | 21 October 2016 |
Plasma waves in two-dimensional electron channels: propagation and trapped modesAuthors: Boris Pavlov, VI Ryzhii, IA Semenikhin |
2006 | AGA | 21 October 2016 |
Inverse spectral and scattering theory for the half-line left definite Sturm-Liouville problemAuthors: Rudi Weikard, Christer Bennewitz, Yaroslav Brown |
2006 | AGA | 21 October 2016 |
Quantum chaos on discrete graphsAuthors: Uzy Smilansky |
2006 | AGA | 21 October 2016 |
On the spectrum of the Dirichlet Laplacian in a narrow stripAuthors: Michael Solomyak, Leonid Friedlander |
2006 | AGA | 21 October 2016 |
3D scanning technology as a standard archaeological tool for pottery analysis: practice and theoryAuthors: Uzy Smilansky, A Karasik |
2006 | AGA | 21 October 2016 |
Equality of Lifshitz and Van Hove exponents on amenable Cayley graphsAuthors: I Veselic, T Antunovic |
2006 | AGA | 21 October 2016 |
Vibration modes of 3n-gaskets and other fractalsAuthors: Alexander Teplyaev, ET Al, B Steinhurst |
2006 | AGA | 21 October 2016 |
Crystals that nature might miss creatingAuthors: Toshikazu Sunada |
2006 | AGA | 21 October 2016 |
On Bernoulli decompositions for random variables, concentration bounds, and spectral localizationAuthors: F Germinet, Abel Klein, Simone Warzel, Michael Aizenman |
2006 | AGA | 21 October 2016 |
Vacuum energy in quantum graphsAuthors: Justin Wilson |
2006 | AGA | 21 October 2016 |
Sharpness of the phase transition and exponential decay of the subcritical cluster sizeAuthors: I Veselic, T Antunovic |
2006 | AGA | 21 October 2016 |
The modulus of continuity of Wegner estimates for random Schrödinger operators on metric graphsAuthors: Michael Gruber, I Veselic |
2006 | AGA | 21 October 2016 |
Minimizing the ground state energy of an electron in a randomly deformed latticeAuthors: M Loss, J Baker, G Stolz |
2006 | AGA | 21 October 2016 |
Index theorems for quantum graphsAuthors: Stephen Fulling, Peter Kuchment, Justin Wilson |
2006 | AGA | 21 October 2016 |
Quantum graphs where back-scattering is prohibitedAuthors: Uzy Smilansky, Brian Winn, Jon Harrison |
2006 | AGA | 21 October 2016 |
On calculation of Kirchhoff coefficients for Helmholtz resonatorAuthors: Boris Pavlov, Jochen Brüning |
2006 | AGA | 21 October 2016 |
Zeta functions of weighted graphs and covering graphsAuthors: Harold Stark, Audrey Terras, MD Horton |
2006 | AGA | 21 October 2016 |
Eigenvalue correlations in continuum one-dimensional Anderson modelsAuthors: Robert Sims, G Stolz |
2006 | AGA | 21 October 2016 |
Optimal Wegner estimates for random Schrödinger operators on metric graphsAuthors: M Helm, I Veselic, Michael Gruber |
2006 | AGA | 21 October 2016 |
Uniform existence of the integrated density of states for combinatorial and metric graphs over ${\mathbb Z}^d$Authors: Daniel Lenz, I Veselic, Michael Gruber |
2006 | AGA | 21 October 2016 |
Monotone unitary familiesAuthors: Daniel Grieser |
2006 | AGA | 21 October 2016 |
Thin tubes in mathematical physics, global analysis and spectral geometryAuthors: Daniel Grieser |
2006 | AGA | 21 October 2016 |
Spectra of graph neighborhoods and scatteringAuthors: Daniel Grieser |
2006 | AGA | 21 October 2016 |
10 January 2007 to 15 January 2007
2 April 2007 to 5 April 2007
10 April 2007 to 13 April 2007
27 May 2007 to 1 June 2007
26 July 2010 to 30 July 2010
Thursday 18th January 2007 | |||
---|---|---|---|
14:30 to 15:30 |
What is a Discrete Complex Analysis on the Equilateral Triangle Lattice? |
Room 1 | |
16:00 to 17:00 | Room 1 |
Tuesday 23rd January 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 1 | ||
16:00 to 17:00 |
Peter Kuchment Texas A&M University |
Room 1 |
Wednesday 24th January 2007 | |||
---|---|---|---|
12:00 to 14:30 | Discussion Room |
Friday 26th January 2007 | |||
---|---|---|---|
11:00 to 12:00 |
Asymptotic aspects of Schreier graphs of self-similar groups |
Room 1 |
Thursday 1st February 2007 | |||
---|---|---|---|
14:30 to 15:30 |
An approximate boundary distance representation and an approximate rec |
Room 1 |
Wednesday 7th February 2007 | |||
---|---|---|---|
16:00 to 17:00 |
Eigenvalue estimates for Schroedinger operators on regular metric trees |
Room 1 | |
Thursday 8th February 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 1 |
Thursday 15th February 2007 | |||
---|---|---|---|
14:30 to 15:30 |
Scattering on a decorated star-graph as a toy model for the spectral theory of automorphic functions |
Discussion Room | |
16:00 to 17:00 | Room 1 |
Friday 16th February 2007 | |||
---|---|---|---|
11:30 to 12:30 |
Leonid Gurvits Los Alamos National Laboratory |
Room 1 |
Wednesday 21st February 2007 | |||
---|---|---|---|
16:00 to 17:00 |
Spectral edges for periodic operators - some quantum graph examples |
Room 1 |
Tuesday 27th February 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 1 |
Thursday 1st March 2007 | |||
---|---|---|---|
16:00 to 17:00 | Room 1 |
Tuesday 6th March 2007 | |||
---|---|---|---|
16:00 to 17:00 |
Audrey Terras University of California, San Diego |
Room 1 |
Wednesday 7th March 2007 | |||
---|---|---|---|
11:30 to 12:30 | Discussion Room | ||
16:00 to 17:00 | Room 1 |
Tuesday 13th March 2007 | |||
---|---|---|---|
14:30 to 15:30 |
Michael Plum |
Room 1 | |
16:00 to 17:00 |
Validated computation tool for Perron-Frobenius eigenvalue using graph theory |
Room 1 |
Thursday 15th March 2007 | |||
---|---|---|---|
14:30 to 15:30 |
Justin Wilson University of Maryland, College Park |
Room 1 |
Tuesday 20th March 2007 | |||
---|---|---|---|
11:30 to 12:30 |
Carlos Berenstein University of Maryland, College Park |
Room 1 |
Thursday 22nd March 2007 | |||
---|---|---|---|
11:30 to 12:30 | Room 1 | ||
14:30 to 15:30 |
Vadim Kostrykin Johannes Gutenberg-Universität Mainz |
Room 1 | |
Thursday 29th March 2007 | |||
---|---|---|---|
10:30 to 11:30 |
On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators |
Room 2 | |
14:00 to 15:00 | Room 2 |
Monday 16th April 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 1 |
Wednesday 18th April 2007 | |||
---|---|---|---|
14:30 to 15:30 |
Lower bounds of the entropy of quantum limits (after N. Anantharaman and S. Nonnemacher) |
Room 1 |
Thursday 19th April 2007 | |||
---|---|---|---|
14:30 to 15:30 |
Travelling fronts on networks for reaction-diffusion-equations |
Room 1 |
Tuesday 24th April 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 1 |
Thursday 26th April 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 1 | ||
16:00 to 17:00 | Room 1 |
Tuesday 1st May 2007 | |||
---|---|---|---|
16:00 to 17:00 |
Spectral inequalities for a class of hypo-elliptic operators |
Room 1 |
Tuesday 15th May 2007 | |||
---|---|---|---|
14:30 to 15:30 |
Alexander Teplyaev University of Connecticut |
Room 1 |
Thursday 17th May 2007 | |||
---|---|---|---|
14:30 to 15:30 |
Differential operators with singularities and generalised Nevanlinna functions |
Room 1 |
Wednesday 23rd May 2007 | |||
---|---|---|---|
11:00 to 12:00 |
Michael Levitin University of Reading; University College London |
Room 1 | |
16:00 to 17:00 |
Shi Zhou University College London |
Room 1 |
Thursday 24th May 2007 | |||
---|---|---|---|
16:00 to 17:00 |
Volodymyr Nekrashevych Texas A&M University |
Room 1 |
Tuesday 5th June 2007 | |||
---|---|---|---|
14:30 to 15:30 |
Wave propagation in networks of thin fibres: small diameter asymptotics |
Room 1 |
Thursday 7th June 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 1 |
Friday 8th June 2007 | |||
---|---|---|---|
11:00 to 12:00 |
Transition density of Markov processes on fractal-like spaces |
Room 1 |
Tuesday 12th June 2007 | |||
---|---|---|---|
14:30 to 15:30 |
Stanislav Molchanov University of North Carolina |
Room 1 |
Wednesday 13th June 2007 | |||
---|---|---|---|
10:30 to 11:30 | Room 1 | ||
16:00 to 17:00 |
Applications of computer methods and mathematical ideas in archaeology |
Room 1 |
Tuesday 19th June 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 2 | ||
16:00 to 17:00 | Room 2 |
Thursday 21st June 2007 | |||
---|---|---|---|
11:00 to 12:00 |
Ian Wood University of Kent |
Room 1 | |
14:30 to 15:30 |
Bernoulli decompositions for random variables and applications |
Room 1 |
Friday 22nd June 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 1 |
Tuesday 26th June 2007 | |||
---|---|---|---|
14:30 to 15:30 | Room 1 | ||
16:00 to 17:00 | Room 1 |
Saturday 21st March 2015 | |||
---|---|---|---|
11:00 to 12:00 | Room 1 |
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