Speaker: Ian Marshall (HSE)

Date and time: 24.06.2026, 17:00 (Moscow time, GMT +03:00)

Title: Poisson reduction of the space of polygons

Abstract:  For some fixed positive integers N and n (with n < N), we consider the space S(n) of degree n shift operators on a one-dimensional lattice, having periodic coefficients, with period N. An analysis of the space S(n) naturally leads us to look at the space W of twisted polygons; these being sequences of vectors, satisfying v(i+N) = M v(i) for some matrix M. Looking at this from a Poisson point of view, confines us to a restricted class of Poisson structures on W, which in turn generate Possion structures on S(n), providing an alternative - and surprisingly simple - route to results of Frenkel, Reshetikhin, Semenov-Tian-Shansky and Sevostyanov, when they looked at the lattice analogue of the so-called Drinfeld--Sokolov reduction procedure.

It turns out that this slightly different approach to DS reduction generates a sequence of intermediate reductions, all of which yield spaces with bihamiltonian structures.

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