**Speaker**: Anna Lachowska (MIT)

**Title**: Fusion category and beyond

**Abstract**: Starting from a semisimple finite dimensional Lie algebra, we will
consider its quantum deformation with the special value of the
deformation parameter. The finite dimensional representation theory
changes significantly
in this case and becomes richer. In particular,
the fusion category, which has been routinely used in mathematics
and math physics, is only
the "top of the iceberg" of the bigger non-semisimple
category of representations
over the quantum group. Using simple examples, we will look at what
lies beyond.