Charles Boyer Research Interests>
## Charles P. Boyer

#
RESEARCH INTERESTS

My research interests range over a fairly broad part of modern differential
geometry. It interfaces with the theory of Lie groups and both algebraic
geometry and algebraic topology. Recently there have been two main threads.
The first involves the
study of the topology of moduli spaces of holomorphic maps, the so-called
sigma-models, and of the moduli spaces of instantons.

The second uses
contact geometry together with Lie group theoretical methods to give
explicit constructions
of Einstein manifolds of
positive scalar curvature, and then to study the topology of such manifolds.
Very recent work uses methods of algebraic geometry, more specifically
Mori theory, to construct Einstein metrics on 5-manifolds, as well as homotopy
spheres in all odd dimensions. This work appears in my monograph
Sasakian Geometry with K. Galicki published by Oxford University Press.

My earlier work was also two-tiered. The first involved group representation
theory applied to problems of Mathematical Physics, in particular, to the
problem of separation of variables of the partial differential equations that
appear in Mathematical Physics. The second used Lie group methods to study
complex geometry with special applications to general relativity.