Description of the Project

The research project focuses on representation theory, with an emphasis on the study of Lie algebras, W-algebras, quantum groups and their connections to various areas of mathematics and mathematical physics. It spans topics ranging from vertex algebras and Poisson vertex algebras to Yangians and infinite dimensional Lie algebras, from Drinfeld-Jimbo quantum groups to Yangians and affine and toroidal quantum algebras, focusing on their interplay with the theory of integrable systems. A main goal of the project is the construction of fundamental operators, such as R-matrices and K-matrices, and the discovery of new relations between W-algebras and twisted Yangians.

Openings

• 1 year postdoc position at the University of Parma (info). Deadline 14/01/2025.

• 1 year postdoc position at the University of Rome La Sapienza (info). Deadline 19/01/2025.

Publications & preprints

Appel A., Vlaar B., Trigonometric K-matrices for finite-dimensional representations of quantum affine algebras, J. Eur. Math. Soc. (2025), published online first.

https://doi.org/10.4171/jems/1686

Appel A., Vlaar B., Boundary transfer matrices arising from quantum symmetric pairs, Indag. Math. (2025), article online.

https://doi.org/10.1016/j.indag.2025.05.008 

Casarin L., Maffei A., Topological sheaves and spaces of distributions in the global case.

 arXiv:2501.08935 

Casarin L., Maffei A., The Factorizable Feigin-Frenkel center.

arXiv:2501.09589 

Casati M., Valeri D., Multi-component Hamiltonian difference operators. Nonlinearity 38 (2025), 105023.

https://doi.org/10.1088/1361-6544/ae117c

Fairon M., Valeri D., Double Poisson (vertex) algebra cohomology.

arXiv:2509.21232 

Valeri D., Yang D., Remarks on intersection numbers and integrable hierarchies. II. Tau-structure, Proc. R. Soc. A (2025) 20240908.

https://doi.org/10.1098/rspa.2024.0908