Research and Publications
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].
Work-in-progress/Submitted papers/Preprints
The capacity of quiver representations and the Anantharam-Jog-Nair inequality (with Harm Derksen), 2023. [pdf | arxiv]
Hive-type polytopes for quiver semi-invariants and the membership problem for quiver moment cones (with Brett Collins and Dan Kline), 2023. [pdf | arxiv]
Quiver representations of constant Jordan type and vector bundles (with Andrew Carroll and Zongzhu Lin) [pdf | arxiv]
Refereed articles (accepted or published)
Edmonds' problem and the membership problem for orbit semigroups of quiver representations (with Dan Kline), Journal of Pure and Applied Algebra (JPAA), Volume 227, Issue 3, March 2023, 107234. [pdf | doi | arxiv]
A quiver invariant theoretic approach to radial isotropy and the Paulsen problem for matrix frames (with Jasim Ismaeel), SIAM Journal on Applied Algebra and Geometry (SIAGA), Vol. 6, Iss. 4, pp. 536-562, 2022. [pdf | doi | arxiv]
Simultaneous robust subspace recovery and semi-stability of quiver representations (with Dan Kline), Journal of Algebra, Volume 577, 1 July 2021, Pages 210-236. [pdf | doi | arxiv]
The capacity of quiver representations and Brascamp-Lieb constants (with Harm Derksen), International Mathematics Research Notices, 15 September 2021. DOI 10.1093/imrn/rnab064. [pdf | doi | arxiv | Erratum (a few minor publisher notation errors)]
Moduli spaces of representations of special biserial algebras (with Andrew Carroll, Ryan Kinser, and Jerzy Weyman), International Mathematics Research Notices 2020, no. 2, 403-421. [pdf | arxiv]
GIT-equivalence and semi-stable subcategories of quiver representations (with Valerie Granger), Journal of Pure and Applied Algebra, 223(8), 3499-3514, 2019. [pdf | arxiv]
Decomposing moduli of representations of finite-dimensional algebras (with Ryan Kinser), Mathematische Annalen, 372(1), 555-580, 2018. [pdf | arxiv]
On locally semi-simple quiver representations (with Dan Kline), Journal of Algebra, 467 (2016), 284-306. [pdf | arxiv]
Moduli spaces of modules of Schur-tame algebras (with Andrew Carroll), Algebras and Representation Theory, (2015) 18: 961-976. [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. [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. [pdf | arxiv]
On the invariant theory for tame tilted algebras, Algebra & Number Theory, Vol. 7 (2013), No. 1, 193-214. [pdf | arxiv]
On the geometry of orbit closures for representation-infinite algebras, Glasgow Mathematical Journal, 54 (2012), 629-636. [pdf | arxiv]
Geometric characterizations of the representation type of hereditary algebras and of canonical algebras, Advances in Mathematics, 228 (2011), no. 3, 1405-1434. [pdf | arxiv]
Cluster fans, stability conditions, and domains of semi-invariants, Transactions of the American Mathematical Society, 363 (2011), no. 4, 2171-2190. [pdf | arxiv]
Orbit semigroups and the representation type of quivers, Journal of Pure and Applied Algebra, 213 (2009), pp. 1418-1429. [pdf | arxiv]
Quivers, long exact sequences and Horn type inequalities II, Glasgow Mathematical Journal, 51 (2009), 1-17. [pdf | arxiv]
Quivers, long exact sequences and Horn type inequalities, Journal of Algebra, 320 (2008), no. 1, 128-157. [pdf | arxiv]
Counterexamples to Okounkov's log-concavity conjecture (with Harm Derksen and Jerzy Weyman), Compositio Mathematica, 143 (2007), 1545-1557. [arxiv]
Eigenvalues of Hermitian matrices and cones arising from quivers, International Mathematics Research Notices, 2006, Art. ID 59457, 27 pp. [pdf]