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Mathematical Physics, Geometry and Combinatorics Group

The research being pursued by members of the Mathematical Physics and Combinatorics group embraces a broad spectrum of topics of current interest, with particular focus on random matrix theory, quantum information theory, mathematical foundations of quantum mechanics, mesoscopic disordered systems, statistical mechanics, graph theory, matroid theory, and infinite dimensional Riemannian geometry, algebraic geometry and orthogonal polynomials.

The list below highlights a number of the research activities being undertaken, and lists the names of the various members of the group who are active in these areas. For more detailed descriptions of our research as well as other relevant information (collaborations, lists of publications, projects, conference presentations, and so on) please follow the links to the web pages of individual group members.

Research Themes

  • The Tutte polynomial and related graph polynomials (R. Hall, )
  • The computational complexity of graph and matroid problems (R. Hall)
  • Random matrix theory (G. J. RodgersD. V. SavinI. E. Smolyarenko)
  • Structural matroid theory (R. Hall)
  • Resonance scattering and transport in wave chaotic systems (D. V. SavinI. E. Smolyarenko)
  • Complex Networks (G. J. RodgersI. E. Smolyarenko)
  • Mathematical foundations of quantum theory ( S. Virmani)
  • Mathematical theory of quantum information ( S. Virmani)
  • Geometric methods for classical and quantum mechanics ( D. M. Meier)
  • Polynomial inequalities and non-asymptotic bounds for orthogonal polynomials and special functions. (I. Krasikov)
  • Combinatorics, graph theory, reconstruction conjectures, and the 3x+1 problem (I. Krasikov)
  • Bounds on the size of error correcting codes (I. Krasikov)
  • Algebraic geometry, higher dimensional birational geometry, Mirror symmetry, Fano and Calabi-Yau varieties (A. Kaloghiros)
  • Geometric methods for shape analysis, analysis of geometric PDEs, Infinite dimensional Riemannian geometry (M. Bruveris)

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