Mathematical Sciences

Department staff

Professor Alexander Veselov

Photo of Professor Alexander Veselov

Professor of Mathematics

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.
  • 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 “Advances in Mathematical Physics”, “Journal of Nonlinear Mathematical Physics” and “Regular and Chaotic Dynamics”, Editorial Council of “Functional Analysis and Its Applications” and Advisory Board of “Inverse Problems”.

  • Director of Studies, Mathematical Sciences
  • Head of Geometry and Mathematical Physics research group
  • Co-organiser of weekly Geometry and Math Physics seminars and annual “Integrable Days at Loughborough”

Teaching - modules

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

MAD102 - Regular and Chaotic Dynamics - An introductory course on integrable and chaotic dynamics.

Christmas challenges, traditional mathematical challenges for undergraduate students.

Some recent publications

Kemp G.M. and Veselov A.P. "On geometric quantization of Dirac magnetic monopole." J. Nonlin. Math. Phys. 21 (2014), no. 1, 34-42. http://arxiv.org/abs/1203.0766

Feigin M.V., Hallnas M.A and Veselov A.P. "Baker-Akhiezer functions and generalised Macdonald-Mehta integrals." J. Math. Phys. 54 (2013), no. 5, 052106. http://arxiv.org/abs/1203.0766

Mkrtchyan R.L. and Veselov A.P. "Universality in Chern-Simons theory." JHEP, 2012(8), 2012. http://arxiv.org/abs/1203.0766

Mkrtchyan R.L., Sergeev A.N and Veselov A.P. "Casimir eigenvalues for universal Lie algebra." J. Math. Phys., 53(10), 2012.arxiv.org/abs/1105.0115

Felder G., Hemery A.D. and Veselov A.P. "Zeroes of Wronskians of Hermite polynomials and Young diagrams." Physica D, 241(23-24):2131-2137, 2012. arxiv.org/abs/1005.2695

Aguirre L., Felder G. and Veselov A.P. "Gaudin subalgebras and stable rational curves". Compositio Math. 147 (2011), no. 5, 1463-1478. arxiv.org/abs/1004.3253

Sergeev A.N. and Veselov A.P. “Grothendieck rings of basic classical Lie superalgebras”, Annals of Mathematics, 173 (2011), 663-703. arxiv.org/abs/0704.2250

Papageorgiou V.G., Suris Yu.B., Tongas A.G. and Veselov A.P. "On quadrirational Yang-Baxter maps," SIGMA Symmetry Integrability Geom. Methods Appl. 6 (2010), Paper 033, 9 pp. arxiv.org/abs/0911.2895

Sergeev A.N. and Veselov A.P. “BC-infinity Calogero-Moser operator and super Jacobi polynomials”, Adv. Math., Vol. 222 (2009), 1687-1726. arXiv:0807.3858

Sergeev A.N. and Veselov A.P. "Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials"  Comm. Math. Phys., Vol. 288 (2009), 653-675.

Gibbons J. and Veselov A.P. “On the rational monodromy-free potentials with sextic growth”, J. Math. Phys., Vol. 50 (2009), No.1, 01351 

Felder G. and Veselov A.P. “Baker-Akhiezer function as iterated residue and Selberg-type integral”, Glasgow Math J., Vol. 51 (2009), 59-73. arXiv:0807.3895

Veselov A.P. “A few things I learnt from Jurgen Moser”,  Regular and Chaotic Dynamics,Vol.13 (2008), no.6, 515-524 arXiv:0810.5713

Grosset M.-P. and Veselov A.P. “ Lame equation, quantum Euler top and elliptic Bernoulli polynomials”, Proc. Edinburgh Math. Soc. (Ser. 2), Vol. 51 (2008), Issue 03, 635-650. arXiv:math-ph/0508068 

Grosset M.-P. and Veselov A.P. “Periodic continued fractions and hyperelliptic curves,” J. London Math. Soc. (2) 77 (2008), no.3, 593-606. arXiv:math/0701932

M.V. Feigin, A.P. Veselov “On the geometry of V-systems,”  Amer. Math. Soc. Transl. (2) Vol. 224 (2008), 111-123. arXiv:0710.5729

Felder G. and Veselov A.P. “Polynomial solutions of the Knizhnik--Zamolodchikov equations and Schur--Weyl duality ”, IMRN, Vol. 2007, article ID rnm046, 21 pages. arXiv:math/0610383

Feigin M.V. and Veselov A.P. “Coxeter discriminants and logarithmic Frobenius structures”, Adv. Math. 212 (2007), 143-162.arXiv:math-ph/0512095

A.P.  Veselov  "Yang-Baxter maps: dynamical point of view." In "Combinatorial aspect of integrable systems", 145--167, MSJ Mem., 17, Math. Soc. Japan, Tokyo, 2007. arXiv:math/0612814

Grosset M.-P. and Veselov A.P. “Elliptic Faulhaber polynomials and Lame densities of states” IMRN, 2006, Art. ID62120, 1-31. arXiv:math-ph/0508066

Bolsinov A.V., Dullin H.R., Veselov A.P. “Spectra of Sol-manifolds: arithmetic and quantum monodromy,” Comm. Math. Phys. 264 (2006), n.3, 583-611 arXiv:math-ph/0503046

Kasatani M., Miwa T., Sergeev A.N., Veselov A.P. “Coincident root loci and Jack and Macdonald polynomials for special values of the parameters”. Contemp. Math., 2006, vol. 417, 207-225. arXiv:math/0404079

Papageorgiou V.G., Tongas A.G., Veselov A.P. “Yang-Baxter maps and symmetries of integrable equations on quad-graphs.” J. Math. Physics, 47 (2006), 083502.

Felder G., Veselov A.P. “Coxeter group actions on the complement of hyperplanes and special involutions.” Journal of the European Mathematical Society, 7 (2005), 101-116. arXiv:math/0311190