The principal investigator will work on a construction relating certain tensor categories arising from q-deformations of enveloping algebras of simple Lie algebras and certain tensor categories of a geometrical nature. . He will also work on describing the completion of the local ring at a point X in terms of the cohomology of certain sheaves of dg Lie algebras over X naturally associated to a deformation problem. This research is concerned with a mathematical object called a Lie algebra.
Lie algebras arise from another object called a Lie group.
An example of a Lie group is the rotations of a sphere where one rotation is followed by another. Lie groups and Lie algebras are important in areas involving analysis of sperical motion. More on THIS Work .