Dr Daniele Valeri

  • Lecturer in Mathematics (Mathematics)

email: Daniele.Valeri@glasgow.ac.uk

Room 409, School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow, G12 8QQ

Research interests

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.

Research units

Publications

List by: Type | Date

Jump to: 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013
Number of items: 24.

2021

De Sole, A., Jibladze, M., Kac, V. G. and Valeri, D. (2021) Integrable triples in semisimple Lie algebras. Letters in Mathematical Physics, 111(1), 117. (doi: 10.1007/s11005-021-01456-4)

De Sole, A., Kac, V. G., Jibladze, M. and Valeri, D. (2021) Integrability of classical affine W-algebras. Transformation Groups, 26(2), pp. 479-500. (doi: 10.1007/s00031-021-09645-0)

Valeri, D. (2021) W -algebras via Lax type operators. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P. and Witczak-Krempa, W. (eds.) Quantum Theory and Symmetries: Proceedings of the 11th International Symposium, Montreal, Canada. Series: CRM series in mathematical physics. Springer: Cham, pp. 181-198. ISBN 9783030557768 (doi:10.1007/978-3-030-55777-5_17)

2020

Carpentier, S., De Sole, A., Kac, V. G., Valeri, D. and Van De Leur, J. (2020) p ̲ -reduced Multicomponent KP hierarchy and classical W -algebras W ( gl N , p ̲ ). Communications in Mathematical Physics, 380, pp. 655-722. (doi: 10.1007/s00220-020-03817-x)

De Sole, A., Kac, V. G., Valeri, D. and Wakimoto, M. (2020) Poisson λ-brackets for differential-difference equations. International Mathematics Research Notices, 2020(13), pp. 4144-4190. (doi: 10.1093/imrn/rny242)

De Sole, A., Fedele, L. and Valeri, D. (2020) Generators of the quantum finite W-algebras in type A. Journal of Algebra and Its Applications, 19(9), 2050175. (doi: 10.1142/S0219498820501753)

2019

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, 370, pp. 1019-1068. (doi: 10.1007/s00220-019-03416-5)

Genovese, G., Lucà, R. and Valeri, D. (2019) Invariant measures for the periodic derivative nonlinear Schrödinger equation. Mathematische Annalen, 374(3-4), pp. 1075-1138. (doi: 10.1007/s00208-018-1754-0)

2018

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. 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)

2017

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)

2016

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)

2015

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)

2014

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)

2013

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)

This list was generated on Mon Sep 20 10:33:01 2021 BST.
Number of items: 24.

Articles

De Sole, A., Jibladze, M., Kac, V. G. and Valeri, D. (2021) Integrable triples in semisimple Lie algebras. Letters in Mathematical Physics, 111(1), 117. (doi: 10.1007/s11005-021-01456-4)

De Sole, A., Kac, V. G., Jibladze, M. and Valeri, D. (2021) Integrability of classical affine W-algebras. Transformation Groups, 26(2), pp. 479-500. (doi: 10.1007/s00031-021-09645-0)

Carpentier, S., De Sole, A., Kac, V. G., Valeri, D. and Van De Leur, J. (2020) p ̲ -reduced Multicomponent KP hierarchy and classical W -algebras W ( gl N , p ̲ ). Communications in Mathematical Physics, 380, pp. 655-722. (doi: 10.1007/s00220-020-03817-x)

De Sole, A., Kac, V. G., Valeri, D. and Wakimoto, M. (2020) Poisson λ-brackets for differential-difference equations. International Mathematics Research Notices, 2020(13), pp. 4144-4190. (doi: 10.1093/imrn/rny242)

De Sole, A., Fedele, L. and Valeri, D. (2020) Generators of the quantum finite W-algebras in type A. Journal of Algebra and Its Applications, 19(9), 2050175. (doi: 10.1142/S0219498820501753)

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, 370, pp. 1019-1068. (doi: 10.1007/s00220-019-03416-5)

Genovese, G., Lucà, R. and Valeri, D. (2019) Invariant measures for the periodic derivative nonlinear Schrödinger equation. Mathematische Annalen, 374(3-4), pp. 1075-1138. (doi: 10.1007/s00208-018-1754-0)

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. 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. (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)

Book Sections

Valeri, D. (2021) W -algebras via Lax type operators. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P. and Witczak-Krempa, W. (eds.) Quantum Theory and Symmetries: Proceedings of the 11th International Symposium, Montreal, Canada. Series: CRM series in mathematical physics. Springer: Cham, pp. 181-198. ISBN 9783030557768 (doi:10.1007/978-3-030-55777-5_17)

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)

This list was generated on Mon Sep 20 10:33:01 2021 BST.