Pavel Safronov - R-matrices with a spectral parameter via shifted Poisson structures
Constant (dynamical) R-matrices have a categorical interpretation in terms of braided monoidal categories equipped with a monoidal forgetful functor to the category of vector spaces (Harish—Chandra bimodules). In the first part of the talk I will review analogous interpretations of classical rmatrices in terms of shifted Poisson structures. In the second part I will describe a conjectural interpretation of classical (dynamical) r-matrices with a spectral parameter (describing Yangians, quantum affine algebras and elliptic quantum groups) in terms of shifted Poisson structures and their quantizations.