Papers and Preprints:

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

1. "Trivial extension DG-algebras, unitally positive $A_\infty$-algebras, and applications" (with J. Karmazyn and E. Lepri). pdf
2. "Noncommutative singularity theory" (with G. Brown). pdf
3. "Derived deformation theory of crepant curves" (with G. Brown), J. Topol. 17 (2024), no. 4, Paper No. e12359, 42 pp. pdf
4. "Spherical objects in dimensions two and three" (with W. Hara), to appear JEMS. pdf
5. "Local normal forms of noncommutative functions" (with G. Brown). pdf
6. "GV and GW invariants via the enhanced movable cone" (with N. Nabijou), to appear Moduli pdf
7. "A lockdown survey on cDV singularities", Adv. Stud. Pure Math. 88, Mathematical Society of Japan, Tokyo, 2023, 47--93. pdf
8. "Double bubble plumbings and two-curve flops" (with I. Smith), Selecta Math. (N.S.) 29 (2023), no. 2, Paper No. 29, 62 pp. pdf
9. "Tits cone intersections and applications" (with O. Iyama). draft pdf
10. "Stability conditions for contraction algebras" (with J. August), Forum Math. Sigma 10 (2022), Paper No. e73, 20 pp. pdf
11. "Stringy K\"ahler moduli, mutation and monodromy" (with W. Donovan), to appear J. Differential Geom. pdf
12. "Stability conditions for 3-fold flops" (with Y. Hirano), Duke Math. J. 172 (2023), no. 16, 3105--3173. pdf
13. "Gopakumar--Vafa invariants do not determine flops" (with G. Brown), Comm. Math. Phys. 361 (2018), no. 1, 143--154. pdf
14. "Faithful actions from hyperplane arrangements" (with Y. Hirano), Geom. & Topol. 22 (2018), no. 6, 3395--3433. pdf
15. "Noncommutative enhancements of contractions" (with W. Donovan), Adv. Math. 344 (2019), 99--136. pdf
16. "Gorenstein modifications and Q-Gorenstein rings" (with Dao, Iyama and Takahashi), J. Algebraic Geom. 29 (2020), no. 4, 729--751. pdf
17. "Noncommutative Resolutions using Syzygies" (with Dao, Iyama, Iyengar, Takahashi, and Yoshino), Bull. Lond. Math. Soc. 51 (2019), no. 1, 43--48. pdf
18. "Weighted Projective Lines and Rational Surface Singularities" (with O. Iyama), Épijournal Géom. Algébrique 3 (2019), Art. 13, 51 pp. pdf
19. "Contractions and Deformations" (with W. Donovan), Amer. J. Math. 141 (2019), no. 3, 563--592. pdf
20. "Twists and Braids for General 3-fold Flops" (with W. Donovan), J. Eur. Math. Soc. (JEMS) 21 (2019), no. 6, 1641--1701. pdf
21. "Flops and Clusters in the Homological Minimal Model Program", Invent. Math. 211 (2018), no. 2, 435--521. pdf
22. "Noncommutative Deformations and Flops" (with W. Donovan), Duke Math. J. 165, (2016), no. 8, 1397--1474. pdf
23. "Reduction of triangulated categories and Maximal Modification Algebras for cA_n singularities" (with O. Iyama), J. Reine Angew. Math. 738 (2018), 149--202. pdf
24. "Lectures on Noncommutative Resolutions", Noncommutative algebraic geometry, 239--306, Math. Sci. Res. Inst. Publ., 64, Cambridge Univ. Press, New York, 2016. pdf
25. "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
26. "Singular Derived Categories of Q-factorial terminalizations and Maximal Modification Algebras" (with O. Iyama), Adv. Math. 261 (2014), 85--121. pdf
27. "On the Noncommutative Bondal--Orlov Conjecture" (with O. Iyama), J. Reine Angew. Math. 683 (2013), 119--128. pdf
28. "Maximal Modifications and Auslander-Reiten Duality for Non-isolated Singularities" (with O. Iyama), Invent. Math. 197 (2014), no. 3, 521--586. pdf
29. "A New Triangulated Categrory for Rational Surface Singularities" (with O. Iyama), Illinois J. Math. 55 (2011), no. 1, 325--341. pdf
30. "Reconstruction Algebras of Type D (II)", Hokkaido Math. J. 42 (2013), no. 2, 293--329. pdf
31. "Reconstruction Algebras of Type D (I)", J. Algebra 356 (2012) 158--194. pdf
32. "The GL(2,C) McKay Correspondence", Math. Ann. 350, no. 3 (2011), 631--659. pdf
33. "The Classification of Special Cohen-Macaulay Modules" (with O. Iyama), Math. Z. 265 (2010), no. 1, 41--83. link
34. "Superpotentials and Higher Order Derivations" (with R. Bocklandt and T. Schedler), J. Pure Appl. Algebra 214 (2010), no. 9, 1501--1522. link
35. "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.

Other:

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