Sergey M. Sergeev

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Qualification:

MSc in Theoretical Phyiscs (1989) Chair of Quantum Field Theory and High Energy Physics, Faculty of Physics, Moscow State University

PhD in Theoretical and Mathematical Physics (1991) Institute for High Energy Physics

Advanced PhD (Habilitation) in Mathematics and Mathematical Physics (2002) Steklov Institute for Mathematical Science

Contact: office 06C46, phone 6201 2198,
email Sergey Sergeev at canberra.edu.au

Research interests

  • Exactly Solvable (or Integrable) Systems of classical, statistical & quantum mechanic
  • Continuous/discrete soliton equations
  • Yang-Baxter equation and Quantum Groups
  • Bethe Ansatz and spectral equations
  • Integrable quantum field theory
  • Algebraic geometry methods in classical and quantum solvable models
  • Higher-dimensional integrability, tetrahedron and four-simplex equations
  • Algebraic methods in higher-dimensional integrable models
  • Higher-dimensional spectral (Bethe Ansatz) equations
  • Tetrahedron equation and representation theory of Quantum Groups
  • Discrete-Quantum Geometry

Research summary:

My research interests in Mathematics and Mathematical Physics include exactly solvable systems of classical, statistical and quantum mechanics, continuous/discrete soliton equations, Yang-Baxter equation, Bethe Ansatz, Quantum Groups, integrable quantum field theory, algebraic geometry methods in classical and quantum solvable models, higher-dimensional integrability, tetrahedron and four-simplex equations, algebraic methods in higher-dimensional integrable models, higher-dimensional Bethe Ansatz equations, tetrahedron equation and representation theory of Quantum Groups, Discrete-Quantum Geometry.

My main contribution to the theory of quantum integrable systems is the development of the three-dimensional extension of the Quantum Inverse Scattering Method. It includes in particular the discovery of algebraic structures of the tetrahedron equation – the multidimensional generalization of the famous Yang-Baxter equation.

In pure mathematics, the three-dimensional methods provide algebraic structures beyond quantum groups and Hopf algebras. Also, my recent results in this field establish a close connection between multidimensional quantum integrability and geometry. In physics, the quantum integrable models in 2+1 dimensional space-time have a potentially big impact in three-dimensional integrable field theories, topological field theories, quantum membranes and quantum surface effects of condensed matter physics. Due to their close relation to the geometry, these models provide the long expected link to Quantum Gravity.

More research information is available on the mathematical physics and geometry at UC web page.

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