Alexander P. Veselov

Contact Information

Research Area and Interests



Christmas Challenges

Mathematical Physics Seminars

Maths Challengers

Links to the Journals


Professor of Mathematics




Department of Mathematical Sciences 
Loughborough University 
LE11 3TU 


+44 (0)1509 222866


+44 (0)1509 223969


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Research Area

Integrable Systems and Geometry

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.

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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.

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.

Mkrtchyan R.L. and Veselov A.P. "Universality in Chern-Simons theory." JHEP, 2012(8), 2012.

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

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.

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

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

Etingof P., Felder G., Ma X. and Veselov A.P. "On elliptic Calogero-Moser systems for complex crystallographic reflection groups." Journal of Algebra, 329 (2011), 107-129.

Veselov A.P. "On Darboux-Treibich-Verdier potentials." Lett. Math. Phys. 96 (2011), no. 1-3, 209–216.

Sergeev A.N. and Veselov A.P. "Quantum Calogero-Moser systems: a view from infinity", In "XVI Intern. Congress on Math Physics (Prague, August 2009)", 333-337. World Sci., 2010. arXiv:0910.5463

Mkrtchyan R.L. and Veselov A.P. "On duality and negative dimensions in the theory of Lie groups and symmetric spaces. " J. Math. Physics, 52 (2011), 083514.

Sergeev A.N. and Veselov A.P. "Euler characters and super Jacobi polynomials", Adv. Math. 226 (2011), 4286-4315. arXiv:0905.2603

Hemery A.D. and Veselov A.P. "Whittaker-Hill equation and semifinite-gap Schroedinger operators", J. Math.Phys. 51 (2010), no. 7, 072108, 17 pp. arXiv:0906.1697

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.

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, 013513

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

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Teaching - Modules



Number theory

An introduction in the classical number theory.



Regular and Chaotic Dynamics

An introductory course on integrable and chaotic dynamics.

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Christmas Challenges

Traditional mathematical challenges for undergraduate students.

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Mathematical Physics Seminars

These are held on Wednesdays at 4pm in room W002. The main research areas covered in this seminar include geometry in a wide sense, classical and quantum integrable systems, mathematical physics.

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Maths Challengers

The Saturday Maths Masterclasses for local schoolchildren.

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Links to the Journals

Inverse Problems

Regular and Chaotic Dynamics

Advances in Mathematical Physics

Journal of Nonlinear Mathematical Physics


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Department of Mathematical Sciences

Loughborough University