Professor Price will consider some questions in the theory of operator algebras related to the index theory for semigroups of endomorphisms. In this work Professor Price will continue his work with Jorgensen on their extension of the Arveson-Powers index to a setting which assigns an index to certain derivations on operator algebras. He expects to continue his work with Powers on a related problem of analyzing the generator extensions of the second quantization of a symmetric unbounded operator. He also will study isomorphism invariants for a class of operator algebras whose structure resembles that of a one parameter family of Cuntz algebras. Finally Price will continue his project of acquainting undergraduates with certain research topics involving operator algebras. Professor Price's project involves self-adjoint operator algebras. These objects consist of families of Hilbert space operators (infinite matrices of complex numbers) which have an interesting property: the algebra is generated by operators whose value in any state on the algebra is a real number. This property makes these algebras important for physics and indeed physics was the original motivation for their study.
