This project will study unique continuation for subelliptic operators, Wiener's criterion and Harnack inequalities, and symmetry of boundary value problems. Unique continuation for subelliptic operators will be studied through a blend of geometric and variational techniques that allow more cases than the usual Carleman method. In the studies of symmetries the PI will continue his attempts in the solution to Schiffer's conjecture and Pompeiu's problem. The questions to be considered in this project are motivated by basic problems in geometry and mathematical physics. Their answers will contribute to a firmer understanding of fundamental scientific issues.
