Shuffle algebras have long provided important tools in the study of quantum groups. We plan to cover an exciting development of this construction, in which Feigin-Odesskii type shuffle algebras are used to study quantum loop groups, which has already had numerous applications to the theory of integrable systems, geometric representation theory, Macdonald polynomial theory, algebraic combinatorics and especially mathematical physics. However, many aspects of the general theory are still unsolved, such as how to use shuffle algebras in order to give a complete definition of quantum loop groups for arbitrary Kac-Moody types, how to construct PBW bases in these algebras, calculate their R-matrices and classify their representations. By combining lecture series and advanced talks aimed at graduate students and postdocs, we aim to stimulate the next stage in the development of this promising theory.
Mini-courses by David Hernandez and Alexander Tsymbaliuk.
Talks by Misha Bershtein, Benjamin Enriquez, Alexandr Garbali, Nicolle Gonzalez, Iva Halacheva, Duncan Laurie, Anna Pun (to be confirmed).
