Dr Daniele Valeri
School of Mathematics & Statistics
Lecturer in Mathematics (Mathematics)
email: Daniele.Valeri@glasgow.ac.uk
My research interests lie in the interplay between representation theory and mathematical physics. In particular, I like to use algebraic techniques, coming from Lie theory and vertex algebra theory, to approach problems arising in mathematical physics, such as applications to (quantum and classical) integrable systems, Conformal Field Theory and invariant measures for dynamical systems.
Integrable Systems and Mathematical Physics
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De Sole, A., Kac, V. G., Valeri, D. and Wakimoto, M. (2019) Local and non-local multiplicative Poisson vertex algebras and differential-difference equations. Communications in Mathematical Physics, (Accepted for Publication)
De Sole, A., Kac, V. G. and Valeri, D. (2018) A Lax type operator for quantum finite W-algebras. Selecta Mathematica - New Series, 24(5), pp. 4617-4657. (doi:10.1007/s00029-018-0439-6)
De Sole, A., Kac, V. G., Valeri, D. and Wakimoto, M. (2018) Poisson λ-brackets for differential-difference equations. International Mathematics Research Notices, (Accepted for Publication)
Genovese, G., Lucà, R. and Valeri, D. (2018) Invariant measures for the periodic derivative nonlinear Schrödinger equation. Mathematische Annalen, (Accepted for Publication)
De Sole, A., Kac, V. G. and Valeri, D. (2018) Classical affine W-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras. Communications in Mathematical Physics, 360(3), pp. 851-918. (doi:10.1007/s00220-018-3142-8)
De Sole, A., Kac, V. G. and Valeri, D. (2018) Finite W-algebras for glN. Advances in Mathematics, 327, pp. 173-224. (doi:10.1016/j.aim.2017.06.016)
Masoero, D., Raimondo, A. and Valeri, D. (2017) Bethe Ansatz and the spectral theory of affine Lie algebra–valued connections II: the non simply–laced case. Communications in Mathematical Physics, 349(3), pp. 1063-1105. (doi:10.1007/s00220-016-2744-2)
De Sole, A., Kac, V. G. and Valeri, D. (2016) Classical affine W-algebras for glN and associated integrable Hamiltonian hierarchies. Communications in Mathematical Physics, 348(1), pp. 265-319. (doi:10.1007/s00220-016-2632-9)
De Sole, A., Kac, V. G. and Valeri, D. (2016) A new scheme of integrability for (bi)Hamiltonian PDE. Communications in Mathematical Physics, 347(2), pp. 449-488. (doi:10.1007/s00220-016-2684-x)
Genovese, G., Lucà, R. and Valeri, D. (2016) Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation. Selecta Mathematica - New Series, 22(3), pp. 1663-1702. (doi:10.1007/s00029-016-0225-2)
Masoero, D., Raimondo, A. and Valeri, D. (2016) Bethe Ansatz and the spectral theory of affine Lie algebra-valued connections I. The simply-laced case. Communications in Mathematical Physics, 344(3), pp. 719-750. (doi:10.1007/s00220-016-2643-6)
De Sole, A., Kac, V. G. and Valeri, D. (2016) Structure of classical (finite and affine) W-algebras. Journal of the European Mathematical Society, 18(9), pp. 1873-1908. (doi:10.4171/JEMS/632)
De Sole, A., Kac, V. G. and Valeri, D. (2015) Double Poisson vertex algebras and non-commutative Hamiltonian equations. Advances in Mathematics, 281, pp. 1025-1099. (doi:10.1016/j.aim.2015.05.011)
De Sole, A., Kac, V. G. and Valeri, D. (2015) Adler-Gelfand-Dickey approach to classical W-Algebras within the theory of Poisson vertex algebras. International Mathematics Research Notices, 2015(21), pp. 11186-11235. (doi:10.1093/imrn/rnv017)
De Sole, A., Kac, V. G. and Valeri, D. (2014) Dirac reduction for Poisson vertex algebras. Communications in Mathematical Physics, 321(3), pp. 1155-1190. (doi:10.1007/s00220-014-2103-0)
De Sole, A., Kac, V. G. and Valeri, D. (2014) Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents. Communications in Mathematical Physics, 331(2), pp. 623-676. (doi:10.1007/s00220-014-2049-2)
De Sole, A., Kac, V. G. and Valeri, D. (2014) Integrability of Dirac reduced bi-Hamiltonian equations. In: Anconca, V. and Strickland, E. (eds.) Trends in Contemporary Mathematics. Series: Springer INdAM series (8). Springer: Cham, pp. 13-32. ISBN 9783319052533 (doi:10.1007/978-3-319-05254-0_2)
Valeri, D. (2014) Classical W-algebras within the theory of Poisson vertex algebras. In: Gorelik, M. and Papi, P. (eds.) Advances in Lie Superalgebras. Series: Springer INdAM series (7). Springer: Cham, pp. 203-221. ISBN 9783319029511 (doi:10.1007/978-3-319-02952-8_12)
De Sole, A., Kac, V. G. and Valeri, D. (2013) Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras. Communications in Mathematical Physics, 323(2), pp. 663-711. (doi:10.1007/s00220-013-1785-z)
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