- 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
- The Le Bruyn-Procesi theorem and Hilbert schemes with Ryo Yamagishi.
- Birational geometry of quiver varieties and other GIT quotients with Gwyn Bellamy and Travis Schedler.
- Gale duality and the linearisation map for noncommutative crepant resolutions.
Submitted. A talk I gave 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.
To appear Journal of Algebraic Geometry. A talk I gave 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.
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. 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.
geometry of symplectic quotient singularities with Gwyn
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.
linear series and recollement with Yukari Ito and Joseph
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.
Dream Spaces as fine moduli of quiver representations with
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,
- 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
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.