Speaker:  Evgeny Mukhin (IUPUI)

Title: Characters, q-characters, and qq-characters.

Abstract:  The q-characters of finite dimensional modules of affine quantum groups  describe the cancellation of poles of transfer matrices in analytic Bethe ansatz. The qq-characters are combinatorial objects which escribe the commutation of deformed W-currents with screening charges in a similar way.

In this talk I will try to give an elementary introduction to the theory of q- and qq-characters, discuss the related combinatorics and outline the main ideas and challenges in the area.