All my papers can also be accessed via my ArXiv profile, and my Google Scholar profile.

- "Derived deformation theory of crepant curves" (with G. Brown). pdf
- "Spherical objects in dimension two and three" (with W. Hara), to appear JEMS. pdf
- "Local normal forms of noncommutative functions" (with G. Brown). pdf
- "GV and GW invariants via the enhanced movable cone" (with N. Nabijou), to appear Moduli pdf
- "A lockdown survey on cDV singularities", Adv. Stud. Pure Math.
**88**, Mathematical Society of Japan, Tokyo, 2023, 47--93. pdf - "Double bubble plumbings and two-curve flops" (with I. Smith), Selecta Math. (N.S.)
**29**(2023), no. 2, Paper No. 29, 62 pp. pdf - "Tits cone intersections and applications" (with O. Iyama). draft pdf
- "Stability conditions for contraction algebras" (with J. August), Forum Math. Sigma
**10**(2022), Paper No. e73, 20 pp. pdf - "Stringy K\"ahler moduli, mutation and monodromy" (with W. Donovan), to appear J. Differential Geom. pdf
- "Stability conditions for 3-fold flops" (with Y. Hirano), Duke Math. J.
**172**(2023), no. 16, 3105--3173. pdf - "Gopakumar--Vafa invariants do not determine flops" (with G. Brown), Comm. Math. Phys.
**361**(2018), no. 1, 143--154. pdf - "Faithful actions from hyperplane arrangements" (with Y. Hirano), Geom. & Topol.
**22**(2018), no. 6, 3395--3433. pdf - "Noncommutative enhancements of contractions" (with W. Donovan), Adv. Math.
**344**(2019), 99--136. pdf - "Gorenstein modifications and Q-Gorenstein rings" (with Dao, Iyama and Takahashi), J. Algebraic Geom.
**29**(2020), no. 4, 729--751. pdf - "Noncommutative Resolutions using Syzygies" (with Dao, Iyama, Iyengar, Takahashi, and Yoshino), Bull. Lond. Math. Soc.
**51**(2019), no. 1, 43--48. pdf - "Weighted Projective Lines and Rational Surface Singularities" (with O. Iyama), Épijournal Géom. Algébrique
**3**(2019), Art. 13, 51 pp. pdf - "Contractions and Deformations" (with W. Donovan), Amer. J. Math.
**141**(2019), no. 3, 563--592. pdf - "Twists and Braids for General 3-fold Flops" (with W. Donovan), J. Eur. Math. Soc. (JEMS)
**21**(2019), no. 6, 1641--1701. pdf - "Flops and Clusters in the Homological Minimal Model Program", Invent. Math.
**211**(2018), no. 2, 435--521. pdf - "Noncommutative Deformations and Flops" (with W. Donovan), Duke Math. J.
**165**, (2016), no. 8, 1397--1474. pdf - "Reduction of triangulated categories and Maximal Modification Algebras for cA_n singularities" (with O. Iyama), J. Reine Angew. Math.
**738**(2018), 149--202. pdf - "Lectures on Noncommutative Resolutions", Noncommutative algebraic geometry, 239--306, Math. Sci. Res. Inst. Publ.,
**64**, Cambridge Univ. Press, New York, 2016. pdf - "Frobenius categories, Gorenstein algebras and rational surface singularities" (with O. Iyama, M. Kalck and D. Yang), Compos. Math.
**151**(2015), no. 3, 502--534. pdf - "Singular Derived Categories of Q-factorial terminalizations and Maximal Modification Algebras" (with O. Iyama), Adv. Math.
**261**(2014), 85--121. pdf - "On the Noncommutative Bondal--Orlov Conjecture" (with O. Iyama), J. Reine Angew. Math.
**683**(2013), 119--128. pdf - "Maximal Modifications and Auslander-Reiten Duality for Non-isolated Singularities" (with O. Iyama), Invent. Math.
**197**(2014), no. 3, 521--586. pdf - "A New Triangulated Categrory for Rational Surface Singularities" (with O. Iyama), Illinois J. Math.
**55**(2011), no. 1, 325--341. pdf - "Reconstruction Algebras of Type D (II)", Hokkaido Math. J.
**42**(2013), no. 2, 293--329. pdf - "Reconstruction Algebras of Type D (I)", J. Algebra
**356**(2012) 158--194. pdf - "The GL(2,C) McKay Correspondence", Math. Ann.
**350**, no. 3 (2011), 631--659. pdf - "The Classification of Special Cohen-Macaulay Modules" (with O. Iyama), Math. Z.
**265**(2010), no. 1, 41--83. link - "Superpotentials and Higher Order Derivations" (with R. Bocklandt and T. Schedler), J. Pure Appl. Algebra
**214**(2010), no. 9, 1501--1522. link - "Reconstruction Algebras of Type A", Trans. Amer. Math. Soc.
**363**(2011), 3101--3132. pdf

My talk on derived deformations of curves at HIM.

Noncommutative singularity theory talk at Banff.

My LAGOON talk on double-bubble plumbings and two-curve flops.

My talk to the African Mathematics Seminar, and Banff, Moscow, on the Tits Cone intersection preprint above (and bits of stability conditions).

My Utah talk on the Homological MMP.

Some videos of my older work on 3-folds: Edinburgh, Simons Center and Banff.

Much less recent videos on my work on surfaces can be found Durham and Tokyo.

- "Autoequivalences for 3-fold flops: an overview", Proceedings of Kinosaki Symposium on Algebraic Geometry (2018), 105--112. pdf
- My lectures on Noncommutative Resolutions, written in 2012.
- I intend to write a new survey article in 2019/20. It will appear here.
- Some (now old!) notes from Nagoya in 2008: Lecture 1, Lecture 2, Lecture 3, Lecture 4.
- The (very) elementary proof that the Somos 5 sequence is integer valued.