# Publications and preprints.

## Publications

- Factorization on generalized Calogero-Moser spaces. Journal of Algebra 321 (1), (2009) 338-344. (arXiv)
- On singular Calogero-Moser spaces. Bulletin of the London Mathematical Society 41 (2), (2009) 315-326. (arXiv)
- Cuspidal representations of rational Cherednik algebras at t=0. Mathematische Zeitschrift 269 (3-4), (2011) 609-627. (arXiv)
- The Calogero-Moser partition for G(m,d,n). Nagoya Mathematical Journal 207 (2012), 47-77. (arXiv)
- On Deformation Quantizations of Hypertoric Varities. Pacific Journal of Mathematics 260 (2012), no. 1, 89-127. (arXiv, joint with T. Kuwabara)
- Some combinatorial identities related to commuting varieties and Hilbert schemes. Math. Ann. 335 (2013), no. 3, 801-847. (arXiv, joint with V. Ginzburg and includes an appendix by E. Zoque)
- A new linear quotient of C^4 admitting a symplectic resolution. Math. Zeit. 273 (2013), no. 3-4, 735-769. (arXiv, joint with T. Schedler)
- On the smoothness of centres of rational Cherednik algebras in positive characteristic. Glasg. Math. Journal 55 (2013), no. A, 27-54. (arXiv, joint with M. Martino)
- Affinity of Cherednik algebras on projective space, Algebra and Number Theory 8 (2014), no. 5, 1151–1177. (arXiv, joint with M. Martino)
- Endomorphisms of Verma modules for rational Cherednik algebras. Transform. Groups 19 (2014), no. 3, 699-720. (arXiv)
- Hamiltonian reduction and nearby cycles for Mirabolic D-modules. Adv. Math. 269 (2015), 71–161. (arXiv, joint with V. Ginzburg)
- Counting resolutions of symplectic quotient singularties. Compositio Mathematica 152 (2016), no. 1, 99-114. (arXiv and erratum)
- Cuspidal Calogero-Moser and Lusztig families for Coxeter groups. Journal of Algebra 462 (2016), 197–252. (arXiv, joint with Ulrich Thiel)
- On the (non-)existsence of symplectic resolutions for imprimitive symplectic reflection groups. Mathematical Research Letters 23 (6) (2016), 1537-1564. (arXiv, joint with T. Schedler)
- Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties. Geometry & Topology 21 (5) (2017), 2601-2682. (arXiv, joint with C. Dodd, K. McGerty and T. Nevins)
- SL2-action on Hilbert schemes and Calogero-Moser spaces. Michigan Journal of Mathematics 66 (3) (2017), 519-532. (arXiv, joint with Victor Ginzburg)
- Filtrations on Springer fiber cohomology and Kostka polynomials. Letters in Mathematical Physics 108 (3) (2018), 679–698. (arXiv, joint with Travis Schedler)
- Highest weight theory for finite-dimensional graded algebras with triangular decomposition. Adv. Math. 330 (2018), 361–419. (arXiv, joint with Ulrich Thiel)
- Rational Cherednik algebras and
Schubert cells. Algebras and Representation Theory (2018), 1-35. (arXiv)

- Hyperplane arrangements associated to symplectic quotient singularities. Banach Center Publications 116 (2018), 25-45. (arXiv, joint with Travis Schedler and Ulrich Thiel)
- On symplectic resolutions and factoriality of Hamiltonian reductions. Math. Ann. 375 no. 1-2, (2019), 165–176. (arXiv, joint with Travis Schedler)
- The (cyclic) enhanced nilpotent cone via quiver representations. Manuscripta Math. 159, 279 (2019). (arXiv, joint with Magdalena Boos)
- Theori Cynrychioliad a Hynodion Cyniferydd Symplegol. Gwerddon, 29, October 2019, 81–98. (Translation)
- Birational geometry of symplectic quotient singularities Invent. Math. 222 (2020), no. 2, 399–468. (arXiv, joint with Alastair Craw)
- Semi-simplicity of the category of admissible D-modules. Kyoto J. Math. 61, no. 1, 115–170 (2021). (arXiv, joint with Magdalena Boos)
- Symplectic resolutions of Quiver varieties. Selecta Math. (N.S.) 27 no. 3 (2021). (arXiv, joint with Travis Schedler)
- Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution. Math. Z. 300 (2022), no. 1, 661–681. (arXiv, joint with Johannes Schmitt and Ulrich Thiel)

## Preprints

- Projective generation for equivariant D-modules. (arXiv, joint with Sam Gunningham and Sam Raskin)
- Cores of graded algebras with triangular decomposition. (arXiv, joint with Ulrich Thiel)
- Symplectic resolutions of character varieties. (arXiv, joint with Travis Schedler)
- Cellularity of endomorphism algebras of tilting objects. (arXiv, joint with Ulrich Thiel)
- Invariant holonomic systems on symmetric spaces and other polar representations. (arXiv, joint with Thierry Levasseur, Tom Nevins and Toby Stafford)
- Quantum Hamiltonian Reduction for Polar Representations. (arXiv, joint with Tom Nevins and Toby Stafford)
- On Parabolic Subgroups of Symplectic Reflection Groups. (arXiv, joint with Johannes Schmitt and Ulrich Thiel)
- All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces. (arXiv, joint with Alastair Craw, Steven Rayan, Travis Schedler and Hartmut Weiss)
- A new family of isolated symplectic singularities with trivial local fundamental group. (arXiv, joint with Cédric Bonnafé, Baohua Fu, Daniel Juteau, Paul Levy, Eric Sommers)

## Other work

- Symplectic singularties and their quantizations. Lecture notes (updated 10/09/2018) on mini-course given at the University of Padova, September 3rd-7th 2018. (pdf)
- Y grŵp cymesur. Introductory talk given at the Welsh Mathematics Colloquium, Gregynog, 23rd-25th May 2016. (pdf)
- From Platonic solids to quivers(*). Introductory lecture notes on Platonic solids, reflection groups and quivers, given at the LMS Undergraduate Summer School 2015. (pdf, exercises, solutions)
- Symplectic reflection algebras. Introductory lecture notes on symplectic reflection algebras. (arXiv)
- Exercises on rational Cherednik algebras and Catalan combinatorics. These are exercise on rational Cherednik algebras, written for the AIM workshop "Rational Catalan combinatorics". (pdf)
- Generalized Calogero-Moser spaces and rational Cherednik algebras. PhD thesis, University of Edinburgh. (pdf)
- Localization in P.I. Rings. 4th year undergraduate project, University of Warwick. (pdf)

My MathSciNet reviews are avaliable here.

(*) These notes are very rough and contain many mistakes - take everything with a pinch of salt! If you have problems accessing any of the articles referenced in these lecture notes, just send me an email and I can send you a copy.