Research: Topology


Topology research at OSU focusses on knot theory and three-dimensional manifolds, using combinatorial, geometric and algebraic tools. Particular topics include triangulations, embedded surfaces and both classical and quantum invariants.
 Research Interests
 
Sean Bowman
Visiting Assistant Professor
I'm interested in the relationship between Dehn surgery and bridge numbers of knots, particularly in the case where the surgery is cosmetic.  More generally I enjoy studying Dehn surgery, Heegaard splittings, and knot invariants.  I also do some work in topological data analysis.
 
William Jaco
Full Professor
B.A., Fairmont State College; M.A., Penn State; Ph.D., Wisconsin, 1968. Low-dimensional topology, Geometric and Combinatorial Group Theory. His primary interest is in the study, understanding, and classification of three-manifolds. The mathematical questions and techniques in low-dimensional topology are very similar to those in geometric and combinatorial group theory. Much of this work involves decision problems, algorithms, and computational complexity. Recent work has been the connection of combinatorial structures to the geometry and topology of three-manifolds.

http://www.math.okstate.edu/~jaco/

 
Weiping Li
Full Professor
B.S., Dalian Institute of Technology; Ph.D., Michigan State, 1992. He is interested in Floer homologies of instantons on 3-manifolds and Lagrangian intersections; semi-infinite homology of infinite Lie algebras; mapping class groups and knot theory.

http://www.math.okstate.edu/~wli/

 
Robert Myers
Full Professor
B.A./M.A./Ph.D., Rice U., 1977. His research area, geometric topology, is the study of spaces called manifolds. These are generalizations of the curves and surfaces encountered in calculus. The subject has close ties to group theory and geometry. One particularly rich source of examples and applications, which is also very accessible and easy to visualize, is knot theory. This is exactly what its name implies: the mathematical study of knotted curves in ordinary space.

http://www.math.okstate.edu/~myersr/

 
Elena Pavelescu
Clinical Instructor
http://www.math.okstate.edu/~paveles
 
Andrei Pavelescu
Visiting Assistant Professor
https://www.math.okstate.edu/~andreip
 
Trenton Schirmer
Visiting Assistant Professor