Mathematical Sciences

Department staff

Professor Alexander Veselov

Photo of Professor Alexander Veselov

Professor of Mathematics

Head of Department

Degrees:

Moscow State University:

  • 1977 MSc (Hons) in Mathematics
  • 1982 PhD (supervisor S.P. Novikov)
  • 1991 Doctor of Science

Employment:

  • Landau Institute for Theoretical Physics, Moscow: 1980-84 Junior Research Fellow
  • Department of Mathematics and Mechanics, Moscow State University: 1984-95 Assistant, Associate and Full Professor
  • School of Mathematics, Loughborough University: 1995-present Professor of Mathematics

Research area

  • Integrable Systems and Geometry
  • Mathematical Physics

Current Research Interests

  • Methods of algebraic geometry in the theory of integrable systems.
  • Logarithmic Frobenius structures and special hyperplane configurations.
  • Quantum Calogero-Moser systems, KZ equations and representation theory.
  • Algebraic integrability of Schroedinger operators in many dimensions and Huygens' Principle.
  • Integrable systems in geometry and topology. Integrable gradient flows. Solvable spectral problems on manifolds.
  • Painleve-type equations and spectral theory of Schroedinger operators.
  • Hamiltonian formalism, action-angle variables and Riemann surfaces.
  • Discrete integrable systems. Yang-Baxter maps. Theory of multi-valued groups and iterated correspondences.
  • Solvable algebraic and functional equations.

Member of Editorial Boards of academic journals “Journal of Integrable Systems”, “Journal of Nonlinear Mathematical Physics” and “Regular and Chaotic Dynamics”, Editorial Council of “Functional Analysis and Its Applications

 

  • Head of Department of Mathematical Sciences
  • Head of Geometry and Mathematical Physics research group

Teaching - modules

MAC147 - Number theory - An introduction in the classical number theory.

MAGIC067 Integrable Systems course for PhD students

Christmas challenges, traditional mathematical challenges for undergraduate students.

Some recent publications

 

  1. (with A.N. Sergeev) Dunkl operators at infinity and Calogero-Moser systems. Intern. Math. Res. Notices (2015), rnv002.

  2. (with A.N. Sergeev) Jack-Laurent symmetric functions. Proc. London Math. Society, 111(1) (2015), 63-92.

  3. (with K. Schoebel) Separation coordinates, moduli spaces and Stasheff polytopes. Commun. Math. Phys. 337 (2015), 1255-1274.

  4. (with R. Willox) Burchnall-Chaundy polynomials and Laurent phenomenon. J. Phys. A: Math. Theor. 48 (2015) 205201.

  5. (with A.N. Sergeev) Jack-Laurent symmetric functions for special values of parameters. Glasgow Math. Journal 58(3) (2016), 599-616.

  6. (with L. Aguirre and G. Felder) Gaudin subalgebras and wonderful models. Selecta Mathematica, New Series 22 (3) (2016), 1057-1071.

  7. (with V. Schreiber and J.P. Ward) In search for a perfect shape of poly- hedra: Buffon transformation. L’Enseignement Math`ematique, Vol. 61, fasc. 3-4 (2015), 263-284.

  8. (with W.A. Haese-Hill and M.A. Hallnas) Complex exceptional orthog- onal polynomials and quasi-invariance. Letters Math. Physics 106 (5) (2016), 583-606.

  9. (with W.A. Haese-Hill and M.A. Hallnas) On the spectra of real and complex Lam ́e operators. SIGMA 13(049) (2017)

  10. (with A.N. Sergeev) Symmetric Lie superalgebras and deformed quantum Calogero-Moser problems. Advances in Mathematics 304 (2017), 728-768.

  11. (with A.N. Sergeev) Orbits and invariants of super Weyl groupoid. IMRN Volume 2017(20):6149-6167.

  12. (with M.V. Feigin) -systems, holonomy Lie algebras and logarithmic vector fields. IMRN rnw289 (2017).

  13. (with A. Matsuo) Universal Hilbert series for minimal nilpotent orbit. Proc AMS, Volume 145, Number 12 (2017).

  14. (with K. Spalding) Lyapunov spectrum of Markov and Euclid trees. Nonlinearity 30 (2017), 4428-53.

    15. (with K. Spalding) Growth of values of binary quadratic forms and Conway rivers. Bulletin of the LMS, 50, Issue 3 (2018), 513-528.

    16. (with K. Spalding) Conway river and Arnold sail. Arnold Math. J. Volume 4, Issue 2 (2018), 169-177.