- Dirichlet branes and mirror
symmetry with P.Aspinwall, T.Bridgeland, M.Douglas, M.Gross, A.Kapustin, G.Moore, G.Segal, B.Szendroi, P.M.H.Wilson,
*Clay Mathematics Monographs***4**. AMS, Providence, RI, 2009. x+681 pp.

- (with J. Green) Reconstructing toric quiver flag varieties from a tilting bundle, to appear
*European Journal of Mathematics*.

- (with Y. Ito and J. Karmazyn) Multigraded linear series and recollement, to appear
*Mathematische Zeitschrift*.

- (with S. Cautis and T. Logvinenko) Derived Reid's recipe for
abelian subgroups of SL(3,ℂ),
*Journal für die reine und angewandte Mathematik (Crelle's Journal)***727**(2017), 1-48.

- (with A. Bayer and Z. Zhang) Nef divisors for moduli spaces of complexes with compact support,
*Selecta Mathematica (New Series)***23**(2017), no. 2, 1507-1561.

- (with R. Bocklandt and A. Quintero Vélez) Geometric Reid's recipe for dimer models,
*Mathematische Annalen***361**(2015), 689-723.

- (with A. Quintero Vélez) Cohomology of wheels on
toric varieties,
*Hokkaido Mathematical Journal***44**(2015), 47-79.

- (with
D. Winn) Mori
Dream Spaces as fine moduli of quiver representations,
*Journal of Pure and Applied Algebra***217**(2013), 172-189.

- (with A. Quintero Vélez) Cellular resolutions of noncommutative toric algebras from superpotentials,
*Advances in Mathematics***229**(2012), no. 3., 1516-1554.

- Quiver flag varieties and multigraded linear series,
*Duke Mathematical Journal***156**(2011), no. 3., 469-500.

- The Special McKay correspondence as an equivalence of derived categories,
*Quarterly Journal of Mathematics***62**(2011), 573-591.

- (with G. Smith) Projective toric varieties as fine moduli spaces of quiver representations,
*American Journal of Mathematics***130**(2008), no. 6, 1509-1534.

- (with D. Maclagan and R. Thomas) Moduli of McKay quiver representations II: Grobner basis techniques,
*Journal of Algebra***316**(2007), no. 2, 514-535.

- (with D. Maclagan) Fiber fans and toric quotients,
*Discrete and Computational Geometry***37**(2007), no. 2, 251-266.

- (with D. Maclagan and R. Thomas) Moduli of McKay quiver representations I: the coherent component,
*Proceedings of the London Mathematical Society***95**(2007), no. 1, 179-198.

- An explicit construction of the McKay correspondence for A-Hilb ℂ^3,
*Journal of Algebra***285**(2005), no. 2, 682-705.

- (with A. Ishii) Flops of G-Hilb and
equivalences of derived categories by variation of GIT quotient,
*Duke Mathematical Journal***124**(2004), no. 2, 259-307.

- An introduction to motivic integration, In
*Strings and Geometry*, 203-225, Clay Mathematical Proceedings**3**, AMS, Providence, RI, 2004.

- (with M. Reid) How to
calculate A-Hilb ℂ^3, In
*Geometry of toric varieties*, 129--154, Séminaires et Congrès**6**, SMF, Paris, 2002. - The McKay
correspondence and representations of the McKay quiver,
*University of Warwick Ph.D thesis*, xviii + 134 pp, June 2001.

- Noncommutative
toric geometry,
*Oberwolfach Reports***9**(2012), no. 2, 1254-1257. - Toric varieties are fine moduli spaces,
*Oberwolfach Reports***3**(2006), no. 2, 266-268. - (for W. Fulton) Enumerative Geometry,
*Quantum Field Theory, Supersymmetry, and Enumerative Geometry*(IAS/PCMI, V. 11), AMS (2006). - (for C.H. Clemens) Introduction to Hodge Theory, Appunti dei Corsi Tenuti da Docenti della Scuola. Scuola Normale Superiore, Pisa, 1998. 72 pp.

- Quiver representations in toric geometry, Preprint arXiv:0807.2191 produced following summer schools in 2007.

- The Kodaira vanishing theorem via Hodge theory, These notes accompanied a series of lectures at the University of Warwick in 1998.