Professor Yan will continue his research into multivariable spectral theory through the approach of Hilbert modules. The goal is to apply methods from algebraic geometry, homological algebra, and complex geometry. He will study topological and algebraic invariants of Hilbert modules, the structures of C*- algebras associated with natural Hilbert modules and the spectral theory of subnormal modules. Professor Yan's work involves the theory of C* algebras. The notion of a C* algebra is an abstraction of the idea of a family of linear transformations on a space. These transformations can also be thought of as having values in the states of the space, and the property of this family which is responsible for the symbol * is that the algebra is generated by transformations whose values in these states are real numbers. The fact that these objects appear naturally in many branches of mathematics and physics make them important to study.
