Geometric currents in piezoelectricity.

The seminar concerns a mathematical analysis of piezoelectricity in
slowly deformed crystals. As a simple model for the phenomenon, we
consider a gas of non-interacting electrons subject to a slowly
time-dependent periodic potential. We prove that, in the adiabatic
limit, the piezoelectric current per unit volume is given by the
King-Smith and Vanderbilt formula, and we show how it relates to the
first Chern class of a particular vector bundle.
We then consider a more general case, allowing for a time-dependent
periodicity lattice, and we exhibit some corrections to the King-Smith
and Vanderbilt formula.