Professor Misha Feigin
- Professor of Mathematics (Mathematics)
R440 Level 4, The Mathematics and Statistics Building, University of Glasgow, University Place, Glasgow, G12 8SQ
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.
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)
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
- Castellan, Simone
Star deformations in (Poisson) vertex algebras
- Dean, Lewis
Quantum integrable systems and TQFT
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)
4H Projects "Oil extraction and algebraic domains", "From orthogonal polynomials to random matrices".
2F "Foundations of Pure Mathematics"
4H "Further Complex Analysis"