Qayum Khan
Assistant Professor of Mathematics (Post-doctorate)

Employed at Vanderbilt Since: August 2006 -- July 2009

Highest Degree: Ph.D., Indiana University, July 2006

Mailing Address:

Qayum Khan
Department of Mathematics
1326 Stevenson Center
Vanderbilt University
Nashville, TN 37240 U.S.A.

Office Phone: 615-322-3659 (SC 1531)
Fax: 615-343-0215 (c/o Khan)

Specialization: I am a mathematician working on the classification problem in the topology of high-dimensional manifolds. The main tool is surgery theory, which forms a robust bridge between the combinatorial geometry of compact manifolds and their algebraic structure given by Poincaré duality. I look at the obstructions to deforming a homotopy equivalence between manifolds so that the comparison cleanly splits along a two-sided submanifold. This behavior is necessarily satisfied for any isomorphism between these spaces.
A more sophisticated application to the classification problem concerns equivariant rigidity of an aspherical closed manifold (formally, the equivariant Borel question). Such an application factors through the Farrell-Jones isomorphism conjecture in algebraic topology. This early 1990's conjecture is an active multidisciplinary area of research in the United States, Germany, and the United Kingdom. It was initially verified in the mid 1980's by Farrell and Hsiang for the class of torsion-free, crystallographic groups. Remarkably, splitting obstructions give counterexamples to equivariant rigidity, if the isomorphism conjecture is true and 2-torsion is present.
Look under "Vitae" for a layperson's summary of research goals. The basic goal is to pass from a coarse equivalence to a finer equivalence between smooth shapes.