Publications and preprints.

Publications

  • Factorization on generalized Calogero-Moser spaces, Journal of Algebra 321, 338-344. (arXiv)
  • On singular Calogero-Moser spaces, Bulletin of the London Mathematical Society 41 (2), 315-326. (arXiv)
  • Cuspidal representations of rational Cherednik algebras at t=0. Mathematische Zeitschrift 269 (3-4), 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)

Preprints

  • Rational Cherednik algebras and Schubert cells. (arXiv)
  • Filtrations on Springer fiber cohomology and Kostka polynomials To appear in Letters in Mathematical Physics. (arXiv, joint with Travis Schedler)
  • Symplectic resolutions of Quiver varieties and character varieties. (arXiv, joint with Travis Schedler)
  • The (cyclic) enhanced nilpotent cone via quiver representations. (arXiv, joint with Magdalena Boos)
  • Hyperplane arrangements associated to symplectic quotient singularities. (arXiv, joint with Travis Schedler and Ulrich Thiel)
  • Highest weight theory for finite-dimensional graded algebras with triangular decomposition. (arXiv, joint with Ulrich Thiel)
  • Semi-simplicity of the category of admissible D-modules. (arXiv, joint with Magdalena Boos)
 

Other work

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

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.