I am interested in pure mathematics, with my main research interests being topology, algebraic geometry, and representation theory. Below I outline my recent projects and current directions; download links to project reports and notes are included where available.
Summary: I participated in MIORPA (the Mathematical Institute’s Online Research Projects with Africa), a virtual mentorship programme hosted by the University of Oxford, and worked on a project about quantum groups and their representations supervised by Dr. Duncan Laurie. The project covered an introduction to quantum groups (using the foundational example of Uq(sl2)), and the classification of its finite dimensional representations.
Summary: My final year thesis investigated tangent vectors and tangent bundles for common smooth manifolds including spheres, tori, and smooth graphs. I focused on constructions of tangent spaces as derivations (an abstract formulation that allows for a coordinate-independent analysis), and also explored some properties of the tangent space at a point, which provides a crucial linear approximation of the manifold's local geometry.