Profile

Wajid  has mostly worked in low dimensional topology on a family of conjectures centred around Wall's D(2) problem, which asks if it is possible to have a space (specifically a finite cell complex) which is homologically 2 dimensional, but geometrically 3 dimensional (in the sense that it is not homotopy equivalent to a space of lower dimension).  Other aspects of low dimensional topology that he has worked on include computation of homotopy modules over the fundamental group and finding additional symmetries in the Poincare duality of manifolds.

Much of the algebra used to study these topological problems may be translated to other areas of mathematics and in particular he has done work on the K-theory of cyclotomic fields, and the Borel regulator.  Another direction he has worked in is finding closed model category structures for certain coalgebras and Lie algebras and exploring a unification of Koszul and Morita dualities.

He is currently studying quaternion group representations on lattices in relation to Wall's D(2) problem and applications of knot theory to helping robots deal with tangled cables.  He is also interested in pursuing certain lines of thought concerning topological quantum field theory and exotic R4's.

Research

Research Interests:

Homotopy theory (of cell complexes), representation theory of groups (over Z), quandles, surgery on manifolds, k-invariants over integral group rings, Clifford algebras, Hochschild homology, MC elements, K-theory over cyclotomic fields, Khovanov homology, closed model categories, topological quantum field theories, group presentations.

Publications