Department of Mathematics, Florida State University
PhD, Cornell University, 1987
Office: 114 Love Building
Office Hours: Tuesday and Friday, 11-12.
Telephone: (850) 644-2202
Fax: (850) 644-4053
URL : http://www.math.fsu.edu/~klassen/
Spring 2020 Course:
MAA4227/MAA5307 Advanced Calculus II
Summary of Research Interests
Statistics on Manifolds
Three and Four Dimensional Topology and Geometry. My work
in this area (mostly joint with Paul Kirk of Indiana University) has involved
investigating properties of three and four dimensional manifolds, including
knots in the three-sphere, using the techniques of gauge theory and by
studying representations of their fundamental groups in certain Lie groups.
In particular we have developed techniques of computing spectral flow and
Chern-Simons invariants using representation spaces and algebraic topology.
Riemann Surfaces and Their Moduli Spaces. My interest here
lies in studying the maps between Hurwitz spaces (which are spaces of branched
coverings of the Riemann sphere sharing a common combinatorial description)
and moduli spaces. I am also interested in the geometry and topology of
the moduli spaces themselves, and in certain aspects of the uniformization
Computer Visualization. In recent joint work with Anuj
Srivastava, Washington Mio and others, we are applying ideas from differential
geometry to problems in computer visualization.