Lieb-Robinson Bounds and Applications to Quantum Systems: How Dynamics Controls Statics

I will review a topic in mathematical physics, called Lieb-Robinson bounds, that exemplifies analysis, geometry, and dynamics.  These bounds describe the dynamics of a physical system of many interacting quantum degrees of freedom: they control how rapidly a disturbance can propagate through the system.  The speed of the propagation depends on the geometry of the system.  Then, using elementary ideas in analysis, one can obtain some powerful results on the static properties of the system, such as decay of correlations or quantization of the Hall conductance.  This will be an introductory talk with no specific background required.