Analysis on Graphs and its Applications

by Cambridge University

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.Read more at: http://www.newton.ac.uk/programmes/AGA/

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Recent Episodes
  • A computer-assisted existence proof for photonic band gaps
    Jan 30, 2022 – 49:47
  • A lower bound for nodal count on discrete and metric graphs
    Aug 27, 2008 – 01:02:00
  • A Solution to an Ambarzumyan Problem on Trees
    Jul 29, 2010 – 35:09
  • Absolutely continuous spectrum for trees of finite forward cone type
    Aug 2, 2010 – 45:34
  • Another Martini for quantum graphs
    Jan 30, 2022 – 55:11
  • Applications of computer methods and mathematical ideas in archaeology
    Jan 30, 2022 – 01:03:00
  • Approximations of strongly singular couplings at quantum graph vertices
    May 20, 2008 – 49:50
  • Asymptotic aspects of Schreier graphs of self-similar groups
    Jan 30, 2022 – 58:08
  • Bernoulli decompositions for random variables and applications
    Jan 30, 2022 – 01:01:00
  • Boundary value problems for infinite metric graphs
    Sep 4, 2008 – 01:02:08
  • Characterization of the static response of a two-dimensional elastic network
    Jul 29, 2010 – 17:52
  • Complete characterization and synthesis of the response function of elastodynamic networks
    Jul 29, 2010 – 58:02
  • Contractive semigroups on metric graphs
    Sep 4, 2008 – 01:01:19
  • Convergence of resonances on thin branched quantum wave guides
    Sep 1, 2008 – 33:09
  • Convergence results for thick graphs
    Aug 2, 2010 – 44:23
  • Diffusion in narrow randomly perturbed tubes
    Jan 30, 2022 – 58:39
  • Dirichlet eigenvalues in a narrow strip
    May 19, 2008 – 01:01:44
  • Dirichlet to Neumann Maps for Infinite Metric Graphs
    Jul 30, 2010 – 49:00
  • Dirichlet-to-Neumann techniques for periodic problems
    Aug 2, 2010 – 32:04
  • Discrete alloy type models: averaging and spectral properties
    Jul 30, 2010 – 43:56
  • Eigenvalue estimates for Schroedinger operators on regular metric trees
    Sep 2, 2008 – 37:29
  • Electronic states in ordered and disordered quantum networks: with applications to graphene and to C and B nanotubes
    Mar 20, 2008 – 01:00:17
  • Excitonic influence on transport coefficients in low dimensional quantum systems
    Mar 20, 2008 – 58:54
  • Explicit Formulae Appearing in Graph Zeta Functions
    Jul 29, 2010 – 11:31
  • Explicit Formulas for Zeta Functions of Graphs
    Jul 28, 2010 – 47:36
  • Fat graphs: Variations on a theme
    Jul 29, 2010 – 01:01:09
  • Finding eigenvalues and resonances of the Laplacian on domains with regular ends
    Apr 17, 2008 – 58:03
  • Graphs which sound the same
    Mar 25, 2008 – 53:29
  • Hardy inequalities and asymptotics for heat kernels
    Jul 30, 2010 – 45:05
  • Heat kernel estimates for Laplace operators on metric trees
    Jul 29, 2010 – 36:11
  • Heat kernels on metric graphs and a trace formula
    Sep 2, 2008 – 01:00:07
  • Hyperbolic polynomials and lower bounds in combinatorics
    Jan 30, 2022 – 56:40
  • Index Theorems for Quantum Graphs
    Aug 2, 2010 – 34:47
  • Internet tomography
    Jan 30, 2022 – 01:05:00
  • Inverse scattering problems for quantum graphs
    Mar 25, 2008 – 52:27
  • Inverse spectral problems on compact and noncompact trees
    Sep 4, 2008 – 38:01
  • Is there an interesting index theory for quantum graphs?
    Jan 30, 2022 – 55:12
  • Limits of self-similar graphs and criticality of the Abelian Sandpile Mode
    Jul 30, 2010 – 14:59
  • Line integrals of one-forms on the Sierpinski gasket
    Jul 28, 2010 – 33:36
  • Liouville theorems for equations on coverings of graphs and manifolds
    Jan 30, 2022 – 36:00
  • Localization under external interactions in periodic quantum graphs
    Mar 20, 2008 – 54:52
  • Localized shelf waves on a curved coast - existence of eigenvalues of a linear operator pencil in a curved waveguide
    May 20, 2008 – 49:45
  • Many-particle systems on quantum graphs with singular interactions
    Jul 28, 2010 – 41:30
  • Matrix valued orthogonal polynomials and random walks
    Jan 30, 2022 – 52:46
  • Maximum principle for elliptic inequalities on the stratified sets
    Sep 3, 2008 – 45:30
  • Necklace graphs and slowing down of the light
    Aug 2, 2010 – 53:33
  • Network models for Bose-Einstein condensates
    Sep 3, 2008 – 01:01:15
  • Nodal domains and spectral critical partitions on graphs
    Jul 28, 2010 – 45:22
  • Non-Weyl Asymptotics for Resonances of Quantum Graphs
    Jul 28, 2010 – 01:00:45
  • On control and Inverse problems for the wave equation on graphs
    Sep 2, 2008 – 31:57
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