Current support: Simons Foundation Grant, Award Number 711639 [2020-2025]. Past support: NSA grant H98230-15-1-0022 [2015-2017] and NSF grant DMS-1101383 [2011-2015].

Click here for a more detailed summary of the papers listed below.


Work-in-progress/Submitted papers/Preprints

Edmonds' problem and the membership problem for orbit semigroups of quiver representations
with Dan Kline
Abstract  |  pdf  |  arxiv
Simultaneous robust subspace recovery and semi-stability of quiver representations
with Dan Kline
Abstract  |  pdf  |  arxiv
The capacity of quiver representations and Brascamp-Lieb constants
with Harm Derksen
Abstract  |  pdf  |  arxiv
Quiver representations of constant Jordan type and vector bundles
with Andrew Carroll and Zongzhu Lin
Abstract  |  pdf  |  arxiv
Notes on GIT fans for quivers
Abstract  |  pdf  |  arxiv

Refereed articles (accepted or published)

GIT-equivalence and semi-stable subcategories of quiver representations
with Valerie Granger
Journal of Pure and Applied Algebra, 223(8), 3499-3514, 2019
Abstract  |  pdf  |  arxiv
Decomposing moduli of representations of finite-dimensional algebras
with Ryan Kinser
Mathematische Annalen, 372(1), 555-580, 2018
Abstract  |  pdf  |  arxiv
Moduli spaces of representations of special biserial algebras
with Andrew Carroll, Ryan Kinser, and Jerzy Weyman
International Mathematics Research Notices 2018
Abstract  |  pdf  |  doi  |  arxiv
On locally semi-simple quiver representations
with Dan Kline
Journal of Algebra, 467 (2016), 284-306.
Abstract  |  pdf  |  arxiv
Moduli spaces of modules of Schur-tame algebras
with Andrew Carroll
Algebras and Representation Theory, (2015) 18: 961-976.
Abstract  |  pdf  |  arxiv
On the invariant theory for acyclic gentle algebras
with Andrew Carroll
Transactions of the American Mathematical Society, 367 (2015), no. 5, 3481-3508.
Abstract  |  pdf  |  arxiv
Module varieties and representation type of finite dimensional algebras
with Ryan Kinser and Jerzy Weyman
International Mathematics Research Notices 2015, no 3, 631-650.
Abstract  |  pdf  |  arxiv
On the invariant theory for tame tilted algebras
Algebra & Number Theory, Vol. 7 (2013), No. 1, 193-214.
Abstract  |  pdf  |  arxiv
On the geometry of orbit closures for representation-infinite algebras
Glasgow Mathematical Journal, 54 (2012), 629-636.
Abstract  |  pdf  |  arxiv
Geometric characterizations of the representation type of hereditary algebras and of canonical algebras
Advances in Mathematics, 228 (2011), no. 3, 1405-1434.
Abstract  |  pdf  |  arxiv
Cluster fans, stability conditions, and domains of semi-invariants
Transactions of the American Mathematical Society, 363 (2011), no. 4, 2171-2190.
Abstract  |  pdf  |  arxiv
Orbit semigroups and the representation type of quivers
Journal of Pure and Applied Algebra, 213 (2009), pp. 1418-1429.
Abstract  |  pdf  |  arxiv
Quivers, long exact sequences and Horn type inequalities II
Glasgow Mathematical Journal, 51 (2009), 1-17.
Abstract  |  pdf  |  arxiv
Quivers, long exact sequences and Horn type inequalities
Journal of Algebra, 320 (2008), no. 1, 128-157.
Abstract  |  pdf  |  arxiv
Counterexamples to Okounkov's log-concavity conjecture
with Harm Derksen and Jerzy Weyman
Compositio Mathematica, 143 (2007), 1545-1557.
Abstract  |  arxiv
Eigenvalues of Hermitian matrices and cones arising from quivers
International Mathematics Research Notices, 2006, Art. ID 59457, 27 pp.
Abstract  |  pdf