Lusztig`s PBW bases for finite-type quantum groups are an explicit construction of crystal bases. We now understand that the combinatorics of these bases is best described by MV (Mirković-Vilonen) polytopes. This is especially interesting because MV polytopes also appear in different contexts in different areas in representation theory. In the first part of the lectures, I will recall the finite-type story and explain the relationship with MV polytopes. In the second part, I will recall the affine PBW bases constructed by Beck-Chari-Pressley, Akasaka, and Beck-Nakajima. I will explain how the combinatorics of affine PBW bases is exactly encoded by affine MV polytopes. This is joint work with Peter Tingley. Date: Aug 23 (Mon) 17:00~18:15 (GMT +9, Seoul) Aug 24 (Tue) 17:00~18:15 (GMT +9, Seoul) Place: Zoom online - Link Meetiing ID: 895 4096 7546 PW: QSMS