Publications

Publications

• Coulomb Branches have symplectic singularities. Lett. Math. Phys. 113 (2023), no. 5, Paper No. 104, 8pp. (arXiv)

• The Rank One property for free Frobenius extensions.  (arXiv, joint with Ulrich Thiel)

• A new family of isolated symplectic singularities with trivial local fundamental group. Proc. Lond. Math. Soc. (3) 126 (2023), no. 5, 1496–1521. (arXiv, joint with Cédric Bonnafé, Baohua Fu, Daniel Juteau, Paul Levy, Eric Sommers)

• On Parabolic Subgroups of Symplectic Reflection Groups. Glasg. Math. J. 65 (2023), no. 2, 401–413. (arXiv, joint with Johannes Schmitt and Ulrich Thiel)

• Cellularity of endomorphism algebras of tilting objects.  Adv. Math. 404 (2022), Paper No. 108387, 38 pp. (arXiv, joint with Ulrich Thiel)

• Symplectic resolutions of character varieties. Geom. Topol. 27 (2023), no. 1, 51–86. (arXiv, joint with Travis Schedler)

• Projective generation for equivariant D-modules. Transform. Groups 27 (2022), no. 3, 737–749. (arXiv, joint with Sam Gunningham and Sam Raskin)

• 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)

• Symplectic resolutions of Quiver varieties. Selecta Math. (N.S.) 27 no. 3 (2021). (arXiv, joint with Travis Schedler)

• Semi-simplicity of the category of admissible D-modules. Kyoto J. Math. 61, no. 1, 115–170 (2021). (arXiv, joint with Magdalena Boos)

• Birational geometry of symplectic quotient singularities. Invent. Math. 222 (2020), no. 2, 399–468. (arXiv, joint with Alastair Craw)

• Theori Cynrychioliad a Hynodion Cyniferydd Symplegol. Gwerddon, 29, October 2019, 81–98. (Translation)

• The (cyclic) enhanced nilpotent cone via quiver representations. Manuscripta Math. 159, 279 (2019). (arXiv, joint with Magdalena Boos)

• On symplectic resolutions and factoriality of Hamiltonian reductions. Math. Ann. 375 no. 1-2, (2019), 165–176. (arXiv, joint with Travis Schedler)

• Hyperplane arrangements associated to symplectic quotient singularities. Banach Center Publications 116 (2018), 25-45. (arXiv, joint with Travis Schedler and Ulrich Thiel)

• Rational Cherednik algebras and Schubert cells. Algebras and Representation Theory (2018), 1-35. (arXiv)

• Highest weight theory for finite-dimensional graded algebras with triangular decomposition. Adv. Math. 330 (2018), 361–419. (arXiv, joint with Ulrich Thiel)

• Filtrations on Springer fiber cohomology and Kostka polynomials. Letters in Mathematical Physics 108 (3) (2018), 679–698. (arXiv, joint with Travis Schedler)

• SL2-action on Hilbert schemes and Calogero-Moser spaces. Michigan Journal of Mathematics 66 (3) (2017), 519-532. (arXiv, joint with Victor Ginzburg)

• 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)

• 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)

• Cuspidal Calogero-Moser and Lusztig families for Coxeter groups. Journal of Algebra 462 (2016), 197–252. (arXiv, joint with Ulrich Thiel)

• Counting resolutions of symplectic quotient singularities. Compositio Mathematica 152 (2016), no. 1, 99-114. (arXiv and erratum)

• Hamiltonian reduction and nearby cycles for Mirabolic D-modules. Adv. Math. 269 (2015), 71–161. (arXiv, joint with Victor Ginzburg)

• Endomorphisms of Verma modules for rational Cherednik algebras. Transform. Groups 19 (2014), no. 3, 699-720. (arXiv)

• Affinity of Cherednik algebras on projective space. Algebra and Number Theory 8 (2014), no. 5, 1151–1177. (arXiv, joint with Maurizio Martino)

• On the smoothness of centres of rational Cherednik algebras in positive characteristic. Glasg. Math. Journal 55 (2013), no. A, 27-54. (arXiv, joint with Maurizio Martino)

• A new linear quotient of C^4 admitting a symplectic resolution. Math. Zeit. 273 (2013), no. 3-4, 735-769. (arXiv, joint with Travis Schedler)

• Some combinatorial identities related to commuting varieties and Hilbert schemes. Math. Ann. 335 (2013), no. 3, 801-847. (arXiv, joint with Victor Ginzburg and includes an appendix by E. Zoque)

• On Deformation Quantizations of Hypertoric Varieties. Pacific Journal of Mathematics 260 (2012), no. 1, 89-127. (arXiv, joint with Toshiro Kuwabara)

• The Calogero-Moser partition for G(m,d,n). Nagoya Mathematical Journal 207 (2012), 47-77. (arXiv)

• Cuspidal representations of rational Cherednik algebras at t=0. Mathematische Zeitschrift 269 (3-4), (2011) 609-627. (arXiv)

• On singular Calogero-Moser spaces. Bulletin of the London Mathematical Society 41 (2), (2009) 315-326. (arXiv)

• Factorization on generalized Calogero-Moser spaces. Journal of Algebra 321 (1), (2009) 338-344. (arXiv)

Preprints

• Pull-back and push-forward functors for holonomic modules over Cherednik algebras. (arXiv, joint with Pavel Etingof and Daniel Thompson) 

• Two invariant subalgebras of rational Cherednik algebras. (arXiv, joint with Niall Hird and Misha Feigin)

• Birational geometry of quiver varieties and other GIT quotients. (arXiv, joint with Alastair Craw and Travis Schedler)

• 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)

• All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces. (arXiv, joint with Alastair Craw, Steven Rayan, Travis Schedler and Hartmut Weiss)

• Cores of graded algebras with triangular decomposition. (arXiv, joint with Ulrich Thiel)

Other work

• Symplectic singularities 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)

• A (incomplete) list of talks. 

For data on fake polynomials of complex reflection groups related to my paper "On singular Calogero-Moser spaces" , click 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.