Professor Alexander Veselov
Professor of Mathematics
Head of Department
Moscow State University:
- 1977 MSc (Hons) in Mathematics
- 1982 PhD (supervisor S.P. Novikov)
- 1991 Doctor of Science
- 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
- 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”.
- 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.
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