Mathematical methods of nonlinear Physics




 Many fundamental non-linear models in Classical and Quantum Physics (Fluid,
Nuclear, Condensed Matter and Plasma Physics, Optics, Gravity, Statistical, Quantum
Field and String Theories) are mathematically characterized by their integrability. The
Integrable models, described by PDEs, ODEs, or discrete difference equations (DDEs),
have regular stable solutions with respect to large classes of initial data, characteristic
parameters and, possibly, external perturbations. The identification of integrable
systems and the investigation of their properties is a major area of Theoretical and
Mathematical Physics. The MMNLP research group covers the following topics:

  1. classification/construction of integrable models by algebraic/geometric methods:
    integrable PDEs in enumerative geometry (cohomological field theory and topological
    recursion), their Hamiltonian description, Poisson vertex algebras, representation
  2. constructive methods for exact, asymptotic or approximate solutions of
    initial/boundary value problems of nonlinear PDE/ODE/DDEs;
  3. analytic study of extreme nonlinear phenomena, like development of singularities, gradient
    catastrophes, transitions from/to elliptic/hyperbolic regimes, the dispersive/dissipative
  4. algebras of symmetries and conservation laws, generalized symmetry and W algebras, classical/quantum superintegrability, Frobenius algebras, topological field theories, random matrix models, symmetry preserving discretization;
  5. textures and waves in complex classical and quantum fluids, hydrodynamical models in
    higher dimensions, shock and rogue waves, nonlinear gravity and general relativity
    regimes, phase transitions in real gases.


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September, 26-27 2024

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