Theory of Relativity seminar, Wydział Fizyki UW and DBP NCBJ Philipp Hoehn (Okinawa Institute of Science and Technology, Japan & University College London, UK) "Progress in relational quantum dynamics" Abstract: The problem of time is a notorious conundrum arising in generally covariant quantum theories. In this talk, I will describe progress on several aspects of the problem of time discussed by Isham and Kuchar in their classic reviews 30 years ago. This will include (i) establishing the equivalence of three approaches to relational dynamics (relational observables, Page-Wootters formalism and deparametrizations), (ii) addressing the multiple-choice problem (non-uniqueness of the clock choice), (iii) addressing the global problem (absence of monotonic clocks), (iv) elucidating how to sidestep Unruh's and Wald's claim that realistic quantum clocks have non-vanishing probability to run backwards, and (v) resolving Kuchar's three criticisms against the Page-Wootters formalism. Time permitting, I will also summarize how one can generalize these insights to quantum reference frames for general symmetry groups (i.e. not only temporal reference frames).