I review new tools for the computation of Kaluza-Klein mass spectra associated with compactifications around various background geometries relevant for string theory. This includes geometries with little to no remaining symmetries, hardly accessible to standard methods. The new tools build on exceptional field theory, the duality covariant formulation of supergravity. Among the applications I discuss the stability of several non-supersymmetric AdS4 and AdS3 vacua, as well as Kaluza-Klein spectra around type IIB S-fold backgrounds. Zoom: https://zoom.us/j/98264204601?pwd=Z0xYdG1vVlEwU1M1bDhVcXQvWURPQT09 Meeting ID: 982 6420 4601 Passcode: 196883

I review the recent construction of six-dimensional (1,0) superconformal models with non-abelian gauge couplings for multiple tensor multiplets. A crucial ingredient in the construction is the introduction of higher-rank tensor fields. I discuss various examples and the possible relation to the (2,0) theories underlying the dynamics of multiple M5 branes.