Exceptional points: Mathematical aspects and Krein space related physics (I + II)

In the first one-hour lecture some basic mathematical facts are presented on an introductory level. Specifically, we discuss spectral singularities of various types, projective Hilbert space structures at exceptional points (EPs), Krein spaces and PT quantum mechanics (PTQM) as well as gauged PTQM and PTQM Jaynes-Cummings models.
The second one-hour lecture is devoted to Krein space related physics and some concrete applications. The topics of this lecture are higher-order EPs in PT-symmetric Bose-Hubbard models, the PTQM brachistochrone and entanglement dynamics. Additionally, we briefly comment on EPs in MHD dynamo setups.