Please note the day of the week for this seminar. 

It has been known that bosonic lattice Hamiltonians have the capacity for curious dynamical behavior including in some cases exponentially accelerated information propagation. This talk will present recent progress on the rigorous derivation of upper bounds on the dynamics generated by Bose-Hubbard type Hamiltonians. The results provide bounds on particle propagation as well as Lieb-Robinson type bounds, which control the spreading of quantum information in a more general sense and come with many applications. The talk will cover the physical circumstances under which the qualitative transport behavior changes (e.g., for long-ranged Hamiltonians) and will give a glimpse of the mathematical proof strategy, which is known as the ASTLO (adiabatic spacetime localization observables) approach. We conclude with some open problems. Based on different collaborations with J. Faupin, T. Kuwahara, C. Rubiliani, I.M. Sigal, and J. Zhang