Michael will be undertaking his third year in an undergraduate mathematics degree in 2019, with a second major in computer science. His interests are varied, though currently he loves many and all things that have at least a dash of geometric flavour. Algebraic elements spice up the mix which he also enjoys, but he has recently started looking at certain combinatorial aspects of the world.
Michael enjoys playing games like Diplomacy and DnD, bricking his Linux machine a hundred times and trying to recover it, and is a fairly proficient Tolkien nerd.
Trisecting Hyperbolic 4-Manifolds
There are certain methods which help one determine trisections of manifolds from triangulations and Coxeter constructions. For the known hyperbolic 4–manifolds of
smallest volume, these methods leave a large gap between the theoretical lower bounds on trisection genus and the upper bounds arising from the simplest explicit constructions. The aim of this project is to close this gap, and to determine at least the order of magnitude of the trisection genus for a number of hyperbolic 4–manifolds.