In this talk, we discuss several recent results on relations between various shadowing properties of dynamical systems with discrete and continuous time and structural stability.
Main topics:
(1) C1-interiors of sets of dynamical systems with various shadowing properties;
(2) shadowing properties of smooth vector fields and structural stability;
(3) equivalence of Lipschitz shadowing and structural stability;
(4) relations between periodic shadowing and Omega-stability.

The formal seminar will be followed by an informal more technical discussion for anyone who is interested in the details of the work.