Sergey Sergeev

Dr Sergey SergeevSergey Sergeev

Office: 11C11

Phone: (02) 6201 2198

Fax: (02) 6201 5231

Email: Sergey.Sergeev@canberra.edu.au

Mail:
11C11, Building 11
Faculty of Information Sciences and Engineering
University of Canberra, Bruce ACT 2601

 Research Area

My research interests in Mathematics and Mathematical Physics include:

  • Exactly Solvable (or Integrable) Systems of classical, statistical & quantum mechanic
  • Continuous/discrete soliton equations
  • Yang-Baxter equation and Quantum Groups
  • Bethe Ansatz
  • 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

My main contribution to the theory of quantum integrable systems is the development of three-dimensional extension of Quantum Inverse Scattering Method. It includes in particular a revealing 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 the quantum groups and Hopf algebras. Also, quite 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 potentially big impact to three-dimensional integrable field theories, topological field theories, quantum membranes and quantum surface effects of condensed matter physics. Due to their closest relation to the geometry, these models provide a long expected passage to Quantum Gravity.

Recent Publications

C1 - Article in a scholarly refereed journal

Vladimir, B.V., Mangazeev, V.V. & Sergeev, S.M. (2008). Quantum Geometry of three-dimensional lattices. Journal of Statistical Mechanics: Theory and Experiement, 7, 1-27

Sergeev, S.M. (2008) Tetrahedron equations and nilpotent subalgebras of Uq(sln), Lett. Math. Phys. 83, 231-235

Bazhanov, V.V., Mangazeev, V.V. & Sergeev, S.M. (2008). Exact solution of the Faddeev-Volkov model, Phys. Lett. A  372, 1547—1550

Sergeev, S.M. (2007). Quantization of three-wave equations. J. Phys. A: Math. Theor. 40, 12709–12724

Bazhanov, V.V., Mangazeev, V.V. & Sergeev, S.M. (2007). Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry. Nuclear Physics B 784 [FS] 234–258

Sergeev, S.M. (2007). Evolution operators for quantum chains. J. Phys. A: Math. Theor. 40, F209-F213

Bortz, M. & Sergeev, S.M. (2006). The q-deformed Bose gas: integrability and thermodynamics. Eur. Phys. J. B 51, 395-405

Sergeev, S.M. (2006). Ansatz of Hans Bethe for a two-dimensional Bose gas. J. Phys. A: Math. Gen. 39, 3035-3045

Sergeev, S.M. (2006). Quantum curve in q-oscillator model. International Journal of Mathematics and Mathematical Sciences

Sergeev, S.M. (2006). Integrability of q-oscillator lattice model. Physics Letters A 357, 417-419

Bazhanov, V.V. & Sergeev, S.M. (2006). Zamolodchikov's tetrahedron Equation and Hidden Structure of Quantum Groups, J. Phys. A: Math. Gen. 39, 3295-3310

Sergeev, S.M. (2006). Thermodynamic limit for a spin lattice. Journal of Statistical Physics 123, 1231-1250

Gehlen, G.V., Pakuliak, S. & Sergeev, S.M. (2005). Bazhanov-Stroganov model from 3D approach. J. Phys. A: Math. Gen. 38, 7269-7298

Sergeev, S.M. (2005). Quantization scheme for modular q-difference equations. Theoretical and Mathematical Physics 142, 422-430

E1 - Full written paper - refereed

G. von Gehlen, S. Pakuliak and S. Sergeev, 3-dimensional integrable lattice models and the Bazhanov-Stroganov model. Nankai Tracts in Math. 10: Differential Geometry and Physics, ed. Mo-Lin Ge and Weiping Zhang, World Scientific, Singapore Dec.

Full written paper - non refereed

Sergeev, S. M. (2008). Super-tetrahedra and super-algebras. arXir:0805.4653, Submitted to Journal of Mathematical Physics, 1-27

Published Report, Presentation or Submission

Sergeev, S. M. (2008). Geometry of Quadrilateral Nets: Second Hamiltonian Form. LAN Archive (University of Canberra),

Sergeev, S. M. (2008). Classical integrable field theories in discrete 2+1 dimensional space-time. LAN Archive (Canberra),