We consider algebras defined from quivers with relations that are kth order derivations of a
superpotential, generalizing results of Dubois-Violette to the quiver case. We give a …

By Auslander's algebraic McKay correspondence, the stable category of Cohen-Macaulay
modules over a simple singularity is triangle equivalent to the $1 $-cluster category of the …

We describe the use of pyramid decomposition in Normaliz, a software tool for the
computation of Hilbert bases and enumerative data of rational cones and affine monoids …

Supersymmetric gauge theories have an important but perhaps under-appreciated notion of
a master space, which controls the full moduli space. For world-volume theories of D-branes …

For a finite abelian group G⊂ GL (n, k), we describe the coherent component Yθ of the
moduli space ℳθ of θ‐stable McKay quiver representations. This is a not‐necessarily …

We construct noncommutative Donaldson–Thomas invariants associated with abelian
orbifold singularities by analyzing the instanton contributions to a six-dimensional …

For a variety $ X $ of positive characteristic and a nonnegative integer $ e $, we define its $
e $-th F-blowup to be the universal flattening of the $ e $-iterated Frobenius of $ X $. Thus …

This article is based on my lecture notes from summer schools at the Universities of Utah
(June 2007) and Warwick (September 2007). We provide an introduction to explicit methods …

This paper constructs cellular resolutions for classes of noncommutative algebras,
analogous to those introduced by Bayer and Sturmfels (1998)[2] in the commutative case. To …

We describe the use of pyramid decomposition in Normaliz, a software tool for the
computation of Hilbert bases and enumerative data of rational cones and affine monoids …