Professor Misha Feigin
- Professor of Mathematics (Mathematics)
telephone:
01413306293
email:
Misha.Feigin@glasgow.ac.uk
R440 Level 4, The Mathematics and Statistics Building, University of Glasgow, University Place, Glasgow, G12 8QQ
https://orcid.org/0000-0001-9184-3940Research interests
The area of my research is the theory of integrable systems in relations with algebra, geometry and mathematical physics.
More concretely, I am working on quantum integrable systems of Calogero-Moser type and their relativistic analogues known as Ruijsenaars-Macdonald operators, Baker-Akhiezer functions and Darboux transformations in many dimensions, Hadamard's problem in the theory of Huygens' Principle, Coxeter and other hyperplane arrangements, rings of quasi-invariants, representations of Cherednik algebras, Frobenius manifolds, WDVV equations, theory of random matrices.
Research groups
Publications
Selected publications
Feigin, M. and Hakobyan, T. (2015) On Dunkl angular momenta algebra. Journal of High Energy Physics, 2015, 107. (doi: 10.1007/JHEP11(2015)107)
Feigin, M. and Silantyev, A. (2014) Generalized Macdonald-Ruijsenaars systems. Advances in Mathematics, 250, pp. 144-192. (doi: 10.1016/j.aim.2013.09.001)
Feigin, M. and Johnston, D. (2014) A class of Baker-Akhiezer arrangements. Communications in Mathematical Physics, 328(3), pp. 1117-1157. (doi: 10.1007/s00220-014-1921-4)
Feigin, M. , Lechtenfeld, O. and Polychronakos, A. (2013) The quantum angular Calogero-Moser model. Journal of High Energy Physics, 2013, 162. (doi: 10.1007/JHEP07(2013)162)
Feigin, M. (2012) Generalized Calogero–Moser systems from rational Cherednik algebras. Selecta Mathematica - New Series, 18(1), pp. 253-281. (doi: 10.1007/s00029-011-0074-y)
Feigin, M. and Shramov, C. (2012) On unitary submodules in the polynomial representations of rational cherednik algebras. International Mathematics Research Notices, 15, pp. 3375-3414. (doi: 10.1093/imrn/rnr140)
Feigin, M. and Silantyev, A. (2012) Singular polynomials from orbit spaces. Compositio Mathematica, 148(6), pp. 1867-1879. (doi: 10.1112/S0010437X1200036X)
Feigin, M. and Veselov, A.P. (2007) Logarithmic Frobenius structures and Coxeter discriminants. Advances in Mathematics, 212(1), pp. 143-162. (doi: 10.1016/j.aim.2006.08.010)
Chen, Y. and Feigin, M. (2006) Painlevé IV and degenerate Gaussian unitary ensembles. Journal of Physics A: Mathematical and General, 39(40), pp. 12381-12393. (doi: 10.1088/0305-4470/39/40/007)
Chalykh, O.A., Feigin, M.V. and Veselov, A.P. (1999) Multidimensional Baker-Akhiezer functions and Huygens' principle. Communications in Mathematical Physics, 206(3), pp. 533-566. (doi: 10.1007/PL00005521)
All publications
2024
Feigin, M. , Wang, Z. and Yoshinaga, M. (2024) Integral expressions for derivations of multiarrangements. International Journal of Mathematics, (doi: 10.1142/S0129167X2450085X) (Early Online Publication)
Abe, T., Enomoto, N., Feigin, M. and Yoshinaga, M. (2024) Free reflection multiarrangements and quasi-invariants. International Mathematics Research Notices, 2024(23), pp. 14157-14177. (doi: 10.1093/imrn/rnae236)
Feigin, M. , Kaminski, L. and Strachan, I. A.B. (2024) Legendre transforms for type An and Bn V-systems. Journal of Physics A: Mathematical and Theoretical, 57, 475205. (doi: 10.1088/1751-8121/ad8cb3)
Alkadhem, M. and Feigin, M. (2024) Commutativity equations and their trigonometric solutions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2300), 20240168. (doi: 10.1098/rspa.2024.0168)
Feigin, M. , Valeri, D. and Wright, J. (2024) Flat coordinates of algebraic Frobenius manifolds in small dimensions. Journal of Geometry and Physics, 200, 105151. (doi: 10.1016/j.geomphys.2024.105151)
2022
Feigin, M. and Vrabec, M. (2022) Bispectrality of AG2 Calogero–Moser–Sutherland system. Mathematical Physics, Analysis and Geometry, 25(4), 29. (doi: 10.1007/s11040-022-09440-7)
Feigin, M. and Hakobyan, T. (2022) Algebra of Dunkl Laplace–Runge–Lenz vector. Letters in Mathematical Physics, 112, 59. (doi: 10.1007/s11005-022-01551-0)
2021
Feigin, M. V. , Hallnäs, M. A. and Veselov, A. P. (2021) Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence. Communications in Mathematical Physics, 386(1), pp. 107-141. (doi: 10.1007/s00220-021-04036-8)
2020
Alkadhem, M. and Feigin, M. (2020) Trigonometric V-systems and solutions of WDVV equations. Journal of Physics A: Mathematical and Theoretical, 54, 024002. (doi: 10.1088/1751-8121/abccf8)
Alkadhem, M., Antoniou, G. and Feigin, M. (2020) Solutions of BCn type of WDVV equations. In: Dubrovin Memorial Volume. Series: Proceedings of symposia in pure mathematics. American Mathematical Society. (Accepted for Publication)
2019
Feigin, M. and Vrabec, M. (2019) Intertwining operator for AG2 Calogero-Moser-Sutherland system. Journal of Mathematical Physics, 60(7), 073503. (doi: 10.1063/1.5090274)
Antoniou, G. and Feigin, M. (2019) Supersymmetric V-systems. Journal of High Energy Physics, 2019, 115. (doi: 10.1007/JHEP02(2019)115)
2018
Feigin, M. V. and Veselov, A. P. (2018) ∨-systems, holonomy lie algebras, and logarithmic vector fields. International Mathematics Research Notices, 2018(7), pp. 2070-2098. (doi: 10.1093/imrn/rnw289)
2016
Feigin, M. (2016) The Hilbert series of Λr,s(m). Appendix in Etingof, P., Rains, E. On Cohen–Macaulayness of algebras generated by generalized power sums. Communications in Mathematical Physics, 347(1), pp. 163-182. (doi: 10.1007/s00220-016-2657-0)
Adler, V.E. et al. (2016) Alexander Petrovich Veselov (on his 60th birthday). Russian Mathematical Surveys, 71(6), pp. 1159-1176. (doi: 10.1070/RM9734)
2015
Feigin, M. and Hakobyan, T. (2015) On Dunkl angular momenta algebra. Journal of High Energy Physics, 2015, 107. (doi: 10.1007/JHEP11(2015)107)
Feigin, M. (2015) Propagation of sound waves. In: Andreev, N.N., Konovalov, S.P. and Panyunin, N.M. (eds.) Mathematical Essence [in Russian]. Mathematical Etudes. Institute of Mathematics of the Russian Academy of Sciences. ISBN 9785906825001
2014
Feigin, M. and Johnston, D. (2014) A class of Baker-Akhiezer arrangements. Communications in Mathematical Physics, 328(3), pp. 1117-1157. (doi: 10.1007/s00220-014-1921-4)
Feigin, M. and Silantyev, A. (2014) Generalized Macdonald-Ruijsenaars systems. Advances in Mathematics, 250, pp. 144-192. (doi: 10.1016/j.aim.2013.09.001)
2013
Feigin, M. , Lechtenfeld, O. and Polychronakos, A. (2013) The quantum angular Calogero-Moser model. Journal of High Energy Physics, 2013, 162. (doi: 10.1007/JHEP07(2013)162)
Feigin, M.V. , Hallnäs, M.A. and Veselov, A.P. (2013) Baker-Akhiezer functions and generalised Macdonald-Mehta integrals. Journal of Mathematical Physics, 54(5), 052106. (doi: 10.1063/1.4804615)
2012
Feigin, M. and Silantyev, A. (2012) Singular polynomials from orbit spaces. Compositio Mathematica, 148(6), pp. 1867-1879. (doi: 10.1112/S0010437X1200036X)
Feigin, M. (2012) Generalized Calogero–Moser systems from rational Cherednik algebras. Selecta Mathematica - New Series, 18(1), pp. 253-281. (doi: 10.1007/s00029-011-0074-y)
Feigin, M. and Shramov, C. (2012) On unitary submodules in the polynomial representations of rational cherednik algebras. International Mathematics Research Notices, 15, pp. 3375-3414. (doi: 10.1093/imrn/rnr140)
2009
Feigin, M., Korff, C. and Strachan, I. (2009) Workshop island 3: algebraic aspects of integrability. Introduction to an additional volume of selected papers arising from the conference on algebraic aspects of integrable systems, Island 3, Islay 2007. Glasgow Mathematical Journal, 51(A), pp. 1-3. (doi: 10.1017/S0017089508004734)
Feigin, M. (2009) Trigonometric solutions of WDVV equations and generalized Calogero-Moser-Sutherland systems. Symmetry, Integrability and Geometry: Methods and Applications, 5, 088. (doi: 10.3842/SIGMA.2009.088)
2008
Feigin, M. and Veselov, A.P. (2008) On the geometry of V-systems. In: Buchstaber, V.M. and Krichever, I.M. (eds.) Geometry, Topology, and Mathematical Physics: S. P. Novikov's Seminar: 2006-2007. Series: American Mathematical Society translations; series 2 (224). American Mathematical Society: Providence, R.I., USA, pp. 111-124. ISBN 9780821846742
2007
Feigin, M. and Veselov, A.P. (2007) Logarithmic Frobenius structures and Coxeter discriminants. Advances in Mathematics, 212(1), pp. 143-162. (doi: 10.1016/j.aim.2006.08.010)
2006
Feigin, M. (2006) On the logarithmic solutions of the WDVV equations. Czechoslovak Journal of Physics, 56(10-11), pp. 1149-1153. (doi: 10.1007/s10582-006-0416-8)
Chen, Y. and Feigin, M. (2006) Painlevé IV and degenerate Gaussian unitary ensembles. Journal of Physics A: Mathematical and General, 39(40), pp. 12381-12393. (doi: 10.1088/0305-4470/39/40/007)
2005
Feigin, M. (2005) Bispectrality for deformed Calogero-Moser-Sutherland systems. Journal of Nonlinear Mathematical Physics, 12(Supple), pp. 95-136. (doi: 10.2991/jnmp.2005.12.s2.8)
2004
Feigin, M. (2004) Quasi-invariants of dihedral systems. Mathematical Notes, 76(5), pp. 723-737. (doi: 10.1023/B:MATN.0000049671.38147.7e)
2003
Feigin, M. (2003) Intertwining relations for the spherical parts of generalized Calogero operators. Theoretical and Mathematical Physics, 135(1), pp. 497-509. (doi: 10.1023/A:1023231402145)
Feigin, M. and Veselov, A.P. (2003) Quasi-invariants and quantum integrals of the deformed Calogero-Moser systems. International Mathematics Research Notices, 2003(46), pp. 2487-2511. (doi: 10.1155/S1073792803130826)
2002
Feigin, M. and Veselov, A.P. (2002) Quasi-invariants of Coxeter groups and m-harmonic polynomials. International Mathematics Research Notices, 2002(10), pp. 521-545. (doi: 10.1155/S1073792802106064)
1999
Feigin, M.V. (1999) Singular operators satisfying an intertwining relation. Theoretical and Mathematical Physics, 121(2), pp. 1478-1483.
Chalykh, O.A., Feigin, M.V. and Veselov, A.P. (1999) Multidimensional Baker-Akhiezer functions and Huygens' principle. Communications in Mathematical Physics, 206(3), pp. 533-566. (doi: 10.1007/PL00005521)
1998
Chalykh, O.A., Feigin, M. and Veselov, A.P. (1998) New integrable generalizations of Calogero-Moser quantum problem. Journal of Mathematical Physics, 39(2), pp. 695-703. (doi: 10.1063/1.532347)
1996
Veselov, A.P., Feigin, M.V. and Chalykh, O.A. (1996) New integrable deformations of quantum Calogero-Moser problem. Russian Mathematical Surveys, 51(3), pp. 573-574. (doi: 10.1070/RM1996v051n03ABEH002956)
Articles
Feigin, M. , Wang, Z. and Yoshinaga, M. (2024) Integral expressions for derivations of multiarrangements. International Journal of Mathematics, (doi: 10.1142/S0129167X2450085X) (Early Online Publication)
Abe, T., Enomoto, N., Feigin, M. and Yoshinaga, M. (2024) Free reflection multiarrangements and quasi-invariants. International Mathematics Research Notices, 2024(23), pp. 14157-14177. (doi: 10.1093/imrn/rnae236)
Feigin, M. , Kaminski, L. and Strachan, I. A.B. (2024) Legendre transforms for type An and Bn V-systems. Journal of Physics A: Mathematical and Theoretical, 57, 475205. (doi: 10.1088/1751-8121/ad8cb3)
Alkadhem, M. and Feigin, M. (2024) Commutativity equations and their trigonometric solutions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2300), 20240168. (doi: 10.1098/rspa.2024.0168)
Feigin, M. , Valeri, D. and Wright, J. (2024) Flat coordinates of algebraic Frobenius manifolds in small dimensions. Journal of Geometry and Physics, 200, 105151. (doi: 10.1016/j.geomphys.2024.105151)
Feigin, M. and Vrabec, M. (2022) Bispectrality of AG2 Calogero–Moser–Sutherland system. Mathematical Physics, Analysis and Geometry, 25(4), 29. (doi: 10.1007/s11040-022-09440-7)
Feigin, M. and Hakobyan, T. (2022) Algebra of Dunkl Laplace–Runge–Lenz vector. Letters in Mathematical Physics, 112, 59. (doi: 10.1007/s11005-022-01551-0)
Feigin, M. V. , Hallnäs, M. A. and Veselov, A. P. (2021) Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence. Communications in Mathematical Physics, 386(1), pp. 107-141. (doi: 10.1007/s00220-021-04036-8)
Alkadhem, M. and Feigin, M. (2020) Trigonometric V-systems and solutions of WDVV equations. Journal of Physics A: Mathematical and Theoretical, 54, 024002. (doi: 10.1088/1751-8121/abccf8)
Feigin, M. and Vrabec, M. (2019) Intertwining operator for AG2 Calogero-Moser-Sutherland system. Journal of Mathematical Physics, 60(7), 073503. (doi: 10.1063/1.5090274)
Antoniou, G. and Feigin, M. (2019) Supersymmetric V-systems. Journal of High Energy Physics, 2019, 115. (doi: 10.1007/JHEP02(2019)115)
Feigin, M. V. and Veselov, A. P. (2018) ∨-systems, holonomy lie algebras, and logarithmic vector fields. International Mathematics Research Notices, 2018(7), pp. 2070-2098. (doi: 10.1093/imrn/rnw289)
Feigin, M. (2016) The Hilbert series of Λr,s(m). Appendix in Etingof, P., Rains, E. On Cohen–Macaulayness of algebras generated by generalized power sums. Communications in Mathematical Physics, 347(1), pp. 163-182. (doi: 10.1007/s00220-016-2657-0)
Adler, V.E. et al. (2016) Alexander Petrovich Veselov (on his 60th birthday). Russian Mathematical Surveys, 71(6), pp. 1159-1176. (doi: 10.1070/RM9734)
Feigin, M. and Hakobyan, T. (2015) On Dunkl angular momenta algebra. Journal of High Energy Physics, 2015, 107. (doi: 10.1007/JHEP11(2015)107)
Feigin, M. and Johnston, D. (2014) A class of Baker-Akhiezer arrangements. Communications in Mathematical Physics, 328(3), pp. 1117-1157. (doi: 10.1007/s00220-014-1921-4)
Feigin, M. and Silantyev, A. (2014) Generalized Macdonald-Ruijsenaars systems. Advances in Mathematics, 250, pp. 144-192. (doi: 10.1016/j.aim.2013.09.001)
Feigin, M. , Lechtenfeld, O. and Polychronakos, A. (2013) The quantum angular Calogero-Moser model. Journal of High Energy Physics, 2013, 162. (doi: 10.1007/JHEP07(2013)162)
Feigin, M.V. , Hallnäs, M.A. and Veselov, A.P. (2013) Baker-Akhiezer functions and generalised Macdonald-Mehta integrals. Journal of Mathematical Physics, 54(5), 052106. (doi: 10.1063/1.4804615)
Feigin, M. and Silantyev, A. (2012) Singular polynomials from orbit spaces. Compositio Mathematica, 148(6), pp. 1867-1879. (doi: 10.1112/S0010437X1200036X)
Feigin, M. (2012) Generalized Calogero–Moser systems from rational Cherednik algebras. Selecta Mathematica - New Series, 18(1), pp. 253-281. (doi: 10.1007/s00029-011-0074-y)
Feigin, M. and Shramov, C. (2012) On unitary submodules in the polynomial representations of rational cherednik algebras. International Mathematics Research Notices, 15, pp. 3375-3414. (doi: 10.1093/imrn/rnr140)
Feigin, M., Korff, C. and Strachan, I. (2009) Workshop island 3: algebraic aspects of integrability. Introduction to an additional volume of selected papers arising from the conference on algebraic aspects of integrable systems, Island 3, Islay 2007. Glasgow Mathematical Journal, 51(A), pp. 1-3. (doi: 10.1017/S0017089508004734)
Feigin, M. (2009) Trigonometric solutions of WDVV equations and generalized Calogero-Moser-Sutherland systems. Symmetry, Integrability and Geometry: Methods and Applications, 5, 088. (doi: 10.3842/SIGMA.2009.088)
Feigin, M. and Veselov, A.P. (2007) Logarithmic Frobenius structures and Coxeter discriminants. Advances in Mathematics, 212(1), pp. 143-162. (doi: 10.1016/j.aim.2006.08.010)
Feigin, M. (2006) On the logarithmic solutions of the WDVV equations. Czechoslovak Journal of Physics, 56(10-11), pp. 1149-1153. (doi: 10.1007/s10582-006-0416-8)
Chen, Y. and Feigin, M. (2006) Painlevé IV and degenerate Gaussian unitary ensembles. Journal of Physics A: Mathematical and General, 39(40), pp. 12381-12393. (doi: 10.1088/0305-4470/39/40/007)
Feigin, M. (2005) Bispectrality for deformed Calogero-Moser-Sutherland systems. Journal of Nonlinear Mathematical Physics, 12(Supple), pp. 95-136. (doi: 10.2991/jnmp.2005.12.s2.8)
Feigin, M. (2004) Quasi-invariants of dihedral systems. Mathematical Notes, 76(5), pp. 723-737. (doi: 10.1023/B:MATN.0000049671.38147.7e)
Feigin, M. (2003) Intertwining relations for the spherical parts of generalized Calogero operators. Theoretical and Mathematical Physics, 135(1), pp. 497-509. (doi: 10.1023/A:1023231402145)
Feigin, M. and Veselov, A.P. (2003) Quasi-invariants and quantum integrals of the deformed Calogero-Moser systems. International Mathematics Research Notices, 2003(46), pp. 2487-2511. (doi: 10.1155/S1073792803130826)
Feigin, M. and Veselov, A.P. (2002) Quasi-invariants of Coxeter groups and m-harmonic polynomials. International Mathematics Research Notices, 2002(10), pp. 521-545. (doi: 10.1155/S1073792802106064)
Feigin, M.V. (1999) Singular operators satisfying an intertwining relation. Theoretical and Mathematical Physics, 121(2), pp. 1478-1483.
Chalykh, O.A., Feigin, M.V. and Veselov, A.P. (1999) Multidimensional Baker-Akhiezer functions and Huygens' principle. Communications in Mathematical Physics, 206(3), pp. 533-566. (doi: 10.1007/PL00005521)
Chalykh, O.A., Feigin, M. and Veselov, A.P. (1998) New integrable generalizations of Calogero-Moser quantum problem. Journal of Mathematical Physics, 39(2), pp. 695-703. (doi: 10.1063/1.532347)
Veselov, A.P., Feigin, M.V. and Chalykh, O.A. (1996) New integrable deformations of quantum Calogero-Moser problem. Russian Mathematical Surveys, 51(3), pp. 573-574. (doi: 10.1070/RM1996v051n03ABEH002956)
Book Sections
Alkadhem, M., Antoniou, G. and Feigin, M. (2020) Solutions of BCn type of WDVV equations. In: Dubrovin Memorial Volume. Series: Proceedings of symposia in pure mathematics. American Mathematical Society. (Accepted for Publication)
Feigin, M. (2015) Propagation of sound waves. In: Andreev, N.N., Konovalov, S.P. and Panyunin, N.M. (eds.) Mathematical Essence [in Russian]. Mathematical Etudes. Institute of Mathematics of the Russian Academy of Sciences. ISBN 9785906825001
Feigin, M. and Veselov, A.P. (2008) On the geometry of V-systems. In: Buchstaber, V.M. and Krichever, I.M. (eds.) Geometry, Topology, and Mathematical Physics: S. P. Novikov's Seminar: 2006-2007. Series: American Mathematical Society translations; series 2 (224). American Mathematical Society: Providence, R.I., USA, pp. 111-124. ISBN 9780821846742
Grants
2014 LMS grant for Collaborative series of workshops on Classical and Quantum Integrability to take place in Glasgow, Leeds, Loughborough, £2000
2014 GMJT grant "Recent directions in representation theory", joint with Prof. I. Gordon, £900
2013 LMS grant for Collaborative series of workshops on Classical and Quantum Integrability to take place in Glasgow, Leeds, Loughborough, £2000
2013 GMJT grant “Workshop on integrable systems”, joint with Dr A. Brochier, £1300
2013 GMJT grant “Cherednik algebras, Macdonald functions and geometry”, joint with Dr C. Korff, £1300
2012 LMS grant for Collaborative series of workshops on Classical and Quantum Integrability to take place in Edinburgh, Leeds, Loughborough, £2000
2011-2014 Royal Society grant “From elliptic systems to Frobenius manifolds – 6d theories and AGT”, a team grant for a joint project with ITEP (Moscow), PI, £11,850
2011 LMS grant for Invited Lecture Series 2012 by Prof. A. Borodin, £4000
2011 EMS grant for supporting lectures for the LMS Invited Lecture series, £960
2011 LMS grant for Collaborative series of workshops on Classical and Quantum Integrability to take place in Glasgow, Leeds, Loughborough, £1400
2008-2011 EPSRC grant “Calogero-Moser systems, Cherednik algebras and Frobenius structures”, awarded value at 80% of FEC £292,863
2008 GMJT conference grant, £800
2007 European Science Foundation grant for Island 3 conference, €11,500
Supervision
- Dean, Lewis
Quantum integrable systems and TQFT - Proserpio, Alessandro
Schottky Groups and the construction of higher genus Frobenius manifolds - Vasilev, Mikhail
Quantum-Classical Duality in Integrable Systems - Vrabec, Martin
Relativistic integrable systems and related structures
PhD projects are available in the areas of Algebra, Geometry and Integrable Systems. Please get in touch for more information.
Previous PhD students:
D. Johnston "Quasi-invariants of hyperplane arrangements" (2007 - 2011)
Previous Research Assistants:
Dr A. Silantyev (2008 - 2011)
Dr D. Johnston (2011)
Dr B. Vlaar (2011)
Teaching
4H Projects "Oil extraction and algebraic domains", "From orthogonal polynomials to random matrices".
2F "Foundations of Pure Mathematics"
4H "Further Complex Analysis"