Algebraic Topology

Using ideas from algebra, how can one classify topological spaces?  This is the fundamental question which investigators in Algebraic Topology try to address. Dr. Haniya is interested in the cohomology of n-pointed configuration spaces of complex projective varieties and rational models for the cohomology of such spaces. There is a natural action of the symmetric group on these spaces as well as an induced action on the model which she studies to facilitate computations for cohomology. In particular, her interest is in the cohomology groups of configurations of Rieman surfaces with fewer points and the algebra structure for the cohomology of the unordered configuration spaces. She is also interested in  the area of Categorification, which lies at the cross roads of algebra, geometry, toplogy and representation theory.  In her work Lagrangian Floer theory is used to describe the Fukaya category of a Riemann surface of higher genus, the aim being to categorify the action of the mapping class group on this category.