Séminaires : Séminaire d'Algèbre

I will talk about an, in general conjectural, construction of a X-cluster structure on
certain Hamiltonian reductions of an X-cluster variety. There are two main classes of examples of
such constructions: moduli spaces of framed local systems with special monodromies and phase spaces of
Goncharov-Kenyon integrable systems. The first class includes the phase space of open XXZ chain and
Ruijsenaars integrable systems. The second class includes integrable systems corresponding to the
q-difference Painleve equations.
Based on works in progress and discussions with P. Gavrylenko, A. Marshakov, M. Semenyakin,
A. Shapiro, G. Schrader.

This talk will take place on Zoom only.