Dr. Tian has completed his Ph.D. under the direction of Dr. Palle Jorgensen at the University of Iowa. His research has been focused on the index theory of Hermitian representations of *-algebras. The applications include the study of vector fields, the theory of Dirichlet problems for second order partial differential operators (PDOs), Sturm-Liouville problems, H. Weyl’s limit-point/limit-circle theory, Schrödinger equations, etc.