I worked with Alessio Corti and Al Kasprzyk at Imperial College, London in July-September 2014 funded by the LMS working on various problems involving orbifold del Pezzo surfaces:
primarily...
reconstructing del Pezzos from a given Hilbert series, and the geometrical and combinatorial consequences such a classification has
(for the realisability of a Hilbert series as the Hilbert series of an orbifold del Pezzo surface, and for the quasiperiod collapse of Fano polygons),
considering criteria for the existence of toric degenerations and examples where they do not exist, and
the structure present in a class of cyclic quotient surface singularities called residual singularities that were recently defined by Akhtar and Kasprzyk here.
These are the \(\mathbb{Q}\)-Gorenstein 'unsmoothable' parts of a quotient singularity and hence are central to deformation theoretic and mirror symmetric questions posed about orbifold surfaces.
By the end of my time at Imperial I received the informal title "resident expert on residual surface singularities".
I would like to thank all of the members of the Fano group at Imperial for the welcoming and highly collaborative environment with which I was presented.
Preprints
Reconstruction of orbifold del Pezzo surfaces from Hilbert series
A geometrical explanation of quasi-period collapse
Contributions from quotient singularities on del Pezzo surfaces.
Posters
BrAG 2016.
I am becoming increasingly interested in cluster algebras both intrinsically and for the role they play in mirror symmetry. See here
for a note on how finite-type cluster algebras fit into the network of Dynkin correspondences.
Preprints
Relative realisations of cluster algebras
Pythagorean triples and cluster algebras
Reconciling mutations (mostly survey plus some goodies).
Research.