Short Research Summary: 

I am interested in applying homotopy theory, the study of topological spaces up to continuous deformation, to solve problems in algebra, geometry, and topology. Most of my work revolves around the study of exotic spheres, smooth manifolds which are topologically but not geometrically equivalent (homeomorphic but not diffeomorphic) to spheres with their standard smooth structure. In which dimensions to exotic spheres exist? Do exotic spheres possess smooth rotational symmetry? It turns out that both of these questions are linked to the homotopy theory of projective spaces, which will feature prominently in the lectures. 

Introductory book/lecture notes: Hatcher, Algebraic Topology