Professor Misha Feigin
- Professor of Mathematics (Mathematics)
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. (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 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
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"