Book

• 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.

Publications and preprints

• Hilbert schemes for crepant partial resolutions with Ruth Pugh.
  Submitted.
• Orbifold Quot schemes via the Le Bruyn-Procesi theorem,
  Submitted.
• The semi-invariant ring as the Cox ring of a GIT quotient with Gwyn Bellamy and Travis Schedler.
  Submitted.
• The Le Bruyn-Procesi theorem and Hilbert schemes with Ryo Yamagishi.
  Submitted.
• Birational geometry of quiver varieties and other GIT quotients with Gwyn Bellamy and Travis Schedler.
  Submitted.
• Gale duality and the linearisation map for noncommutative crepant resolutions.
  Submitted. A talk about this paper is here.
• All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces with Gwyn Bellamy, Steven Rayan, Travis Schedler and Hartmut Weiss.
  Journal of Algebraic Geometry 33 (2024), 757-793. A talk about this paper is here.
• An introduction to Hilbert schemes of points on ADE singularities.
  Advanced Studies in Pure Mathematics 88 (2023), McKay correspondence, mutation and related topics, 119-157.
  
• Quot schemes for Kleinian orbifolds with Søren Gammelgaard, Ádám Gyenge and Balázs Szendrői.
  SIGMA 17 (2021), 099, 21 pages. [This note closes a gap in the proof of Proposition 6.1].
• Punctual Hilbert schemes for Kleinian singularities as quiver varieties with Søren Gammelgaard, Ádám Gyenge and Balázs Szendrői.
  Algebraic Geometry 8 (2021) no. 6, 680--704. [Compare Remarks 6.8(2) of this paper.]
• 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 [the Correction is Mathematische Annalen 380, 911–913 (2021)]
  
• 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.

Published reports and lecture notes

• 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.

Unpublished work

• 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.