Eric Klassen

Professor
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
E-mail: klassen@math.fsu.edu
URL : http://www.math.fsu.edu/~klassen/

Spring 2020 Course:

MAA4227/MAA5307 Advanced Calculus II

Summary of Research Interests

• Shape Analysis
• Statistics on Manifolds
• Differential Geometry
• Topology
• Knot Theory
• Global Analysis
• Lie Groups
• Riemann Surfaces

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 problem.

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.