So far my research has focussed on partition combinatorics, in particular problems arising in the geometry of the Hilbert Scheme of points in the plane.


The article A Combinatorial Proof of Buryak-Feigin-Nakajima is published in Volume 30, Issue 3 of the Electronic Journal of Combinatorics. This paper refines Loehr and Warrington's techniques in this paper to also account for cores and quotients, and as a consequence we obtain a purely combinatorial proof of the main result of Buryak, Feigin, and Nakajima's paper. 

The "background" section may be independently useful, as it recalls much of the background on partitions, cores and quotients and is written with those new to the subject in mind.