The Principal Investigator will study asymptotics of the heat equation, eta invariants for operators of odd dimensional manifolds, multiplicative K-theory, and disk bundles. The work to be carried out relates sound and shape. In a broad sense the work seeks to understand what can be learned about the shape of an object from the sound it may emit. M. Kac once asked an innocent sounding question, "Can you hear the shape of a drum". This question has led to the understanding of related questions in many dimensions. Many useful applications have resulted.
