Equivariant Hilbert schemes and partition combinatorics

As a PhD student I study interactions between algebraic geometry and combinatorics, in particular understanding topological properties of orbifold Hilbert schemes via core and quotient partitions and G-constellations. This work is under the supervision of Dr Paul Johnson. I have written an online tutorial (work-in-progress) as background material on the combinatorial aspect of my research.

McKay Correspondence

In 2015 I secured a £1000 grant from the University of Warwick’s Undergraduate Research Support Scheme (URSS) to undertake an 8 week summer research project researching the 3D McKay correspondence. I wrote code to compute McKay quivers for finite subgroups of SL(3,C) which can be found here. This work was under the supervision of Prof Miles Reid (FRS).

Geometry of Syzygies

My master’s thesis gives an introduction to minimal free resolutions and uses Macaulay2 to compute examples of toric varieties to test the Eisenbud-Goto regularity conjecture. This work was under the supervision of Prof Diane Maclagan.