Speaker: Mikhail Chirkov (HSE University, YarSU)

Title: Quantisation ideals and canonical parametrisations of the unipotent group

Date and time:  17.09.2025, 17:00 (GMT +03:00)

Abstract: Quantisation ideals for dynamical systems on the free associative algebra have proven to be an effective tool for solving the problem of deformation quantisation, as well as for obtaining non-deformation quantisation. This talk will provide a brief overview of the history and motivation behind this approach. In our joint work with A.V. Mikhailov and D.V. Talalaev, we generalize this approach to the case of discrete dynamics on the free associative algebra A. This dynamics is defined by a well-known solution of the tetrahedron equation (Case α from Sergeev's list), which is related to the problem of re-parameterisation of the unipotent group N(3, A). As a result, we construct several families of quantisations, analyze their classical limit and obtain canonical integrable systems compatible with re-parameterisations. We have to mention that the charts and re-parameterisations (mutations) form a cluster-like structure, with Poisson brackets that represent a deformation of the log-canonical type.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com