Alexander
P. Veselov
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Post: |
Professor of Mathematics |
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Office: |
W233ma |
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Address: |
Department of Mathematical Sciences |
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Telephone: |
+44 (0)1509 222866 |
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Fax: |
+44 (0)1509 223969 |
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e-mail: |
Research Area
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Integrable Systems and
Geometry
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Current Research
Interests
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Methods of algebraic geometry
in the theory of integrable systems. |
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Quantum Calogero-Moser systems,
KZ equations and representation theory. |
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Algebraic integrability of
Schroedinger operators in many dimensions and Huygens' Principle. |
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Integrable systems in geometry
and topology. Integrable gradient flows. Solvable spectral problems on
manifolds. |
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Painleve-type equations and
spectral theory of Schroedinger operators. |
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Hamiltonian formalism,
action-angle variables and Riemann surfaces. |
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Discrete integrable systems.
Yang-Baxter maps. Theory of multi-valued groups and iterated correspondences. |
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Solvable algebraic and
functional equations. |
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Some
Recent Publications |
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Sergeev A.N. and Veselov A.P. "Quantum
Calogero-Moser systems: a view from infinity", arXiv:09 |
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Sergeev A.N. and Veselov A.P. "Calogero-Moser
operators in infinite dimension", arXiv:0910.1984 (2009) |
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Sergeev A.N. and Veselov A.P. "Euler
characters and super Jacobi polynomials", arXiv:0905.2603 (2009) |
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Sergeev A.N. and Veselov
A.P. "Jacobi-Trudy formula for generalised Schur polynomials", arXiv:0905.2557 (2009) |
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Hemery A.D. and Veselov A.P. "Whittaker-Hill equation and semifinite-gap
Schroedinger operators", arXiv:0906.1697
(2009) |
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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 |
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Sergeev A.N. and Veselov
A.P. "Deformed Macdonald-Ruijsenaars operators and super Macdonald
polynomials" Comm. Math.
Phys., Vol. 288 (2009), 653-675. |
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Gibbons J. and Veselov A.P. “On
the rational monodromy-free potentials with sextic growth”, J. Math. Phys.,
Vol. 50 (2009), No.1, 013513 |
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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 |
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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 |
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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 |
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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 |
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Sergeev A.N. and Veselov A.P. “Grothendieck
rings of basic classical Lie superalgebras”, arXiv:math.RT/0704.2250. arXiv:0704.2250 |
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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 |
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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 |
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Feigin M.V. and Veselov A.P.
“Coxeter discriminants and logarithmic Frobenius structures”, Adv. Math. 212
(2007), 143-162. arXiv:math-ph/0512095 |
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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 |
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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 |
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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 |
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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 |
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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. |
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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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Adler V.E., Veselov A.P.
“Cauchy problem for integrable discrete equations.” Acta Appl. Math., 2004,
vol. 84, 237-262. |
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Sergeev A.N., Veselov A.P. “ Generalised
discriminants, deformed Calogero-Moser-Sutherland operators and super Jack
polynomials.” Adv. Math., 2005, vol. 192, 341-375. arXiv:math-ph/0307036 |
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Veselov A.P., Ward J.P. “On the
real zeroes of the Hurwitz zeta-function and Bernoulli polynomials.” J. Math.
Anal. Appl., 2005, vol. 305, 712-721. |
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Sergeev A.N., Veselov A.P.
"Deformed quantum Calogero-Moser systems and Lie superalgebras."
Comm. Math. Phys. v. 245, 2004, 249-278. |
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Felder G., Veselov A.P.
"Action of Coxeter groups on m-harmonic polynomials and KZ
equations." Moscow Math Journal, vol.3, 2003, no.4, 1269-1291. |
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Feigin M., Veselov A.P. "Quasi-invariants
and quantum integrals of the deformed Calogero-Moser systems" IMRN,
2003, vol. 46, 2487-2511. |
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Penskoi A.V., Veselov A.P.
"Discrete Lagrangian systems on Virasoro group and Camassa-Holm
family". Nonlinearity, 2003, vol. 16, 683-688. |
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Veselov A.P. "Yang-Baxter
maps and integrable dynamics." Physics Letters A, 314 (2003), 214-221. |
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Veselov A.P. "On
generalisations of Calogero-Moser-Sutherland quantum problem and WDVV
equations." J. Math. Phys., 2002, vol. 43, no. 11, 5675-5682. |
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Moser J., Veselov A.P.
"Two-dimensional "discrete hydrodynamics" and Monge-Ampere
equation," Ergodic Theory and Dynamical Systems, 2002, 22, 1575-83. |
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Feigin M.V., Veselov A.P.
"Quasi-invariants of Coxeter groups and m-harmonic polynomials".
Intern. Math. Res. Notices, 2002, No. 10, 521-545. |
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Chalykh O.A., Veselov A.P.
"Locus configurations and V-systems". Physics Letters A 285 , 2001,
339-349. |
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Veselov A.P. "On Stieltjes
relations, PIV hierarchy and complex monodromy." J. Phys A.: Math and
Gen., 2001, v. 34, 3511-3519. |
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Dullin H.R., Richter P.H.,
Veselov A.P. and Waalkens H. "Actions of the Neumann systems via
Picard-Fuchs equations." Physica D, 2001, v.155, 159-183. |
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Fairlie D.B. and Veselov A.P.
"Faulhaber and Bernoulli polynomials and solitons". Physica D,
2001, v. 152-153, 47-50. |
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Ferapontov E.V. and Veselov
A.P. "Integrable Schroedinger operators with magnetic fields:
factorisation method on curved surfaces". Journal of Mathematical
Physics, 2001, v. 42, no. 2, 590-607. |
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Teaching
- Modules |
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MAC147 |
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Number theory |
An introduction in the
classical number theory. |
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MAD102 |
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Regular and Chaotic Dynamics |
An introductory course on
integrable and chaotic dynamics. |
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Traditional
mathematical challenges for undergraduate students. |
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These are held on Mondays at
5pm in room W 190. The main research areas covered in this seminar include
Classical and Quantum Mechanics, General Relativity, Geometry, Integrable
Systems, Inverse Problems, Spectral Theory, Theory of PDE's. |
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The Saturday Maths
Masterclasses for local schoolchildren. |
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Links
to the Journals |
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Journal of Nonlinear Mathematical Physics |