## Sven Bachmann (The University of British Columbia)

** Title:** Adiabatic dynamics and linear response theory for many-body quantum systems.

** Abstract:** The main theme of this lecture series is the understanding of the local non-autonomous
dynamics of interacting, many-body quantum systems. When the driven dynamics is generated by a
time-dependent family of gapped Hamiltonians, and the driving is slow, then an initial ground state
is (parallel) transported within the ground state subspace up to controllable errors (adabatic theorem).
As an application, we shall discuss a rigorous derivation of Kubo’s formula of linear response theory.
If time permits, a proof of quantization of the Hall conductance for such interacting systems will
be sketched.