讲座内容：

A model space is a closed subspace of the Hardy space which is invariant under the backward shift, and a truncated Toeplitz operator is the compression of a Toeplitz operator on a model space. In this talk, we discuss necessary and sufficient conditions  for the commutator of two truncated Toeplitz operators to be compact, and for the product of two truncated Toeplitz operators on a model space to be a compact perturbation of a truncated Toeplitz operator.