- Dirichlet branes and mirror
symmetry with P.Aspinwall, T.Bridgeland, M.Douglas, M.Gross, A.Kapustin, G.Moore, G.Segal, B.Szendrői, P.M.H.Wilson,

*Clay Mathematics Monographs***4**. AMS, Providence, RI, 2009. x+681 pp.

- In preparation:
*Gale duality and the linearisation map for quiver moduli*.

A video of a talk I gave about this paper is available here (connection drops briefly at about 39:00). -
Punctual Hilbert schemes for Kleinian singularities as quiver varieties with Søren Gammelgaard, Ádám Gyenge and Balázs Szendrői.

To appear*Algebraic Geometry*. A talk I gave about this paper is here. - Combinatorial Reid's recipe for consistent dimer models with Liana Heuberger and Jesus Tapia Amador.

*Épijournal de Géométrie Algébrique***5**(2021), Article no. 4. - Birational
geometry of symplectic quotient singularities with Gwyn
Bellamy,

*Inventiones Mathematicae***222**(2020), no. 2, 399-468.

- Reconstructing toric quiver flag varieties from a tilting bundle with James Green,
*European Journal of Mathematics***4**(2018), no. 1, 185-199.

- Multigraded
linear series and recollement with Yukari Ito and Joseph
Karmazyn,
*Mathematische Zeitschrift***289**(2018), no. 1, 535-565.

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

- Derived Reid's recipe for
abelian subgroups of SL(3,ℂ) with Sabin Cautis and Timothy Logvinenko,

*Journal für die reine und angewandte Mathematik***727**(2017), 1-48.

- Geometric Reid's recipe for dimer models with Raf Bocklandt and Alexander Quintero Vélez,

*Mathematische Annalen***361**(2015), 689-723. Erratum.

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

- Mori
Dream Spaces as fine moduli of quiver representations with
Dorothy Winn,

*Journal of Pure and Applied Algebra***217**(2013), 172-189.

- Cellular resolutions of noncommutative toric algebras from superpotentials with Alexander Quintero Vélez,

*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.

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

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

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

- Moduli of McKay quiver representations I: the coherent component with Diane Maclagan and Rekha Thomas,
*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.

- Flops of G-Hilb and
equivalences of derived categories by variation of GIT quotient with Akira Ishii,
*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.

- How to
calculate A-Hilb ℂ^3 with Miles Reid,

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.