My research encompasses equviariant algebraic topology, category theory and graph theory. |
Topology is a kind of geometry that looks at how shapes can stretch and bend into one another. Algebraic topology uses algebra to describe these shapes.
Equivariant topology studies spaces which are symmetric in some way. They might be mirror symmetric, or maybe they can rotate around and end up looking the same, like a circle.
Category theory is the language mathematicians use to talk about structures which are common to different branches of mathematics. Originally developed to discuss connections between algebra and geometry, categorical structures are now spreading into other areas of mathematics.
Graph theory studies discrete structures created by vertices and attached edges.
I am currently working on
applying equivariant techniques to the study of orbifolds. This involves understanding categorical structures such as bicategories of fractions, and also studying geometric groupoids.
I supervised an undergraduate research project (funded by CURM) during the 2020-21 academic year studying applying ideas from homotopy and category theory to graphs. You can watch their presentation of their work on YouTube.
Undergraduate Research with FLC Student Co-Authors: