Integrable Systems

Researchers: Sergey Novikov, Victor Buchstaber, Piotr Grinevich, Boris Dubrovin, Ivan Dynnikov, Oleg Mokhov, Alexey Penskoi, Sergey Smirnov, Dmitry Talalaev and Alexander Veselov.

Research areas:

  • Algebraic geometry and quantum integrable systems (Dmitry Talalaev).
  • Applications of Topology to Mathematical Physics
  • Abelian Functions (Victor Buchstaber)

  • Algebraic geometry and quantum integrable systems

    The so-called "Quantum spectral curve method" is developping since 2004 (Dmitry Talalaev). This approach is focused on construction of the quantum analogs of the algebraic-geometric methods widely used in the classical theory of integrable systems. Till now this generalization was oriented to the class of spin-interaction quantum mechanical models like the Gaudin and Toda systems. The method allows to quantize models, make their solution techniques more effective. Moreover this is related to some interdisciplinary mathematical concept as the Langlands correspondence. At present we explore the non-commutative geometric aspects of this method.