Mark Damuni Williams

Hi! My name is Mark and I'm a computer science PhD student at the University of Nottingham. I study type theory and synthetic mathematics, especially with applications to all different sorts of geometry.

My Research

I work in and around the foundations of maths, looking to set up the axioms in a nice way to make geometry easier! The base system I choose to work in is homotopy type theory, a relatively new foundations for mathematics, in which the basic objects act less like collections of points, and more like topological spaces of points.

My current project involves taking a generic method for constructing synthetic mathematics, that of Grothendieck topologies, and constructing an internal analogue in homotopy type theory. Doing this lets me build internal models of different axioms, and allow two different axiomatic systems to interact.