9704296 Dai This project deals with a variety of problems in the area of spectral geometry and geometric invariants. The investigator is to study manifolds with conical singularity with a view towards defining and understanding certain geometric invariants such as analytic torsion in a more general setting; to study the spectral geometry of degenerating metrics under various processes including the adiabatic limit, and Riemannian collapsing; to study geometric invariants and their behavior under surgery. Spectral geometry is an area where often analytic techniques are used to study geometric objects. This project in particular deals with defining certain geometric invariants via heat equation techniques - the heat equation is among the more well-known partial differential equations, describing the heat flow phenomenon, and much is known about the equation.
