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

- "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), to appear Geometry & Topology. pdf
- "Noncommutative enhancements of contractions" (with W. Donovan) pdf
- "Gorenstein modifications and Q-Gorenstein rings" (with Dao, Iyama and Takahashi) pdf
- "Noncommutative Resolutions using Syzygies" (with Dao, Iyama, Iyengar, Takahashi, and Yoshino) pdf
- "Weighted Projective Lines and Rational Surface Singularities" (with O. Iyama) pdf
- "Contractions and Deformations" (with W. Donovan) pdf
- "Twists and Braids for General 3-fold Flops" (with W. Donovan), to appear JEMS 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 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.

The following are the notes from a series of four lectures I gave in Nagoya in 2008.

Lecture 1, Lecture 2, Lecture 3, Lecture 4

My lectures on Noncommutative Resolutions, written in 2012. I intend to write a new survey article in 2018.

The (very) elementary proof that the Somos 5 sequence is integer valued.