**Dr. Boaz Haberman**

**Department of Mathematics**

**University of Chicago**

** ****ABSTRACT:** What can we infer about physical systems from experimental measurements? I will explore some ill-posed problems where the answer to this question depends subtly on the smoothness of the physical system. In the classical problem of unique continuation, the boundary between uniqueness and nonuniqueness is well-understood. This familiar problem is related to the inverse boundary problem underlying electrical impedance tomography. It is possible to construct certain types of EIT invisibility cloaks, but it is not so clear how singular these cloaks need to be. In the end of the talk, I will discuss some recent results which rule out the existence of certain classes of invisibility cloaks.