We introduce a general model of dimer coverings of certain plane bipartite graphs, which we
call rail yard graphs (RYG). The transfer matrices used to compute the partition function are …

We study the geometry and topology of Hilbert schemes of points on the orbifold surface,
respectively the singular quotient surface, where is a finite subgroup of type A or D. We give …

This is an announcement of conjectures and results concerning the generating series of
Euler characteristics of Hilbert schemes of points on surfaces with simple (Kleinian) …

In this paper we construct an abstract Fock space for general Lie types that serves as a
generalization of the infinite wedge q-Fock space familiar in type A. Specifically, for each …

The affine Grassmannian of admits an embedding into the Sato Grassmannian, which
further admits a Plücker embedding into the projectivization of Fermion Fock space …

When G is a complex reductive algebraic group, MV polytopes are in bijection with the non-
negative tropical points of the unipotent group of G. By fixing w from the Weyl group, we can …

We prove a conjecture of Cautis and Sussan providing a categorification of the Boson-
Fermion correspondence as formulated by Frenkel and Kac. We lift the Bernstein operators …

In this thesis we use classical and modern mathematical techniques to compute generating
functions for plane partitions. We begin by introducing integer partitions and related …

In this dissertation I prove various results that encompass multiple fields. Within higher
representation theory, I categorify the Boson-Fermion correspondence, settling a standing …

This article illustrates Hirota-Sato formalism by establishing that Hirota's direct method is
derivable from Sato theory. This formalism is considered via Maya diagrams and used to …