Publications and editorial work

Editorial Work

I am currently on the Editorial Board of the Canadian Journal of Mathematics, the Canadian Mathematical Bulletin, Algebras and Representation Theory, and PUMP Journal of Undergraduate Research. In addition, I have co-edited the following volumes.

  1. Perspectives in Representation Theory (eds. with Pavel Etingof and Mikhail Khovanov), Contemporary Mathematics 610, Amer. Math. Soc., Providence, RI, 2014.
  2. Geometric Representation Theory and Extended Affine Lie Algebras (eds. with Erhard Neher and Weiqiang Wang), Fields Institute Communications 59, Amer. Math. Soc., Providence, RI, 2011.
  3. Categorification in Representation Theory (eds. with Aaron Lauda and Anthony Licata), International Journal of Mathematics and Mathematical Sciences 2010, Hindawi, 2010.

Publications and preprints

  1. Bubbles in the affine Brauer and Kauffman categories (with Ben Webster), 2024. (arXiv)
  2. The spin Brauer category (with Peter J. McNamara), Forum of Mathematics, Sigma 12 (2024) e98, 1–50. (DOI, arXiv)
  3. Diagrammatics for real supergroups (with Saima Samchuck-Schnarch), Annals of Representation Theory 1 (2024), no. 2, 125–191. (DOI, arXiv)
  4. The quantum isomeric supercategory, Journal of the Institute of Mathematics of Jussieu 23 (2024), no. 3, 1077–1124. (DOI, arXiv)
  5. Quantum diagrammatics for F4 (with Bruce W. Westbury), Journal of Pure and Applied Algebra 228 (2024), no. 11, 107731. (DOI, arXiv)
  6. Diagrammatics for F4 (with Raj Gandhi and Kirill Zainoulline), Bulletin of the London Mathematical Society 55 (2023), no. 1, 349–374. (DOI, arXiv)
  7. Affine oriented Frobenius Brauer categories (with Alexandra McSween), Communications in Algebra 51 (2023), no. 2, 742–756. (DOI, arXiv)
  8. The degenerate Heisenberg category and its Grothendieck ring (with Jonathan Brundan and Ben Webster), Annales scientifiques de l'École normale supérieure (4) 56 (2023), no. 5, 1517–1562. (DOI, arXiv)
  9. Categorification of the elliptic Hall algebra (with Youssef Mousaaid), Documenta Mathematica 27 (2022), 1225–1273. (DOI, arXiv)
  10. Quantum Frobenius Heisenberg categorification (with Jonathan Brundan and Ben Webster), Journal of Pure and Applied Algebra 226 (2022), no. 1, Paper No. 106792, 50 pp. (DOI, arXiv)
  11. Frobenius W-algebras and traces of Frobenius Heisenberg categories (with Michael Reeks), Journal of Algebra and its Applications 21 (2022), no. 2, Paper No. 2250035, 39 pp. (DOI, arXiv)
  12. Affinization of monoidal categories (with Youssef Mousaaid), Journal de l'École polytechnique — Mathématiques 8 (2021), 791–829. (DOI, arXiv)
  13. Frobenius nil-Hecke algebras (with John Stuart), Pacific Journal of Mathematics 311 (2021), no. 2, 455–473. (DOI, arXiv)
  14. Group partition categories (with Samuel Nyobe Likeng), Journal of Combinatorial Algebra 5 (2021), no. 4, 269–406. (DOI, arXiv)
  15. Foundations of Frobenius Heisenberg categories (with Jonathan Brundan and Ben Webster), Journal of Algebra 578 (2021), 115–185. (DOI, arXiv)
  16. Embedding Deligne's category Rep(St) in the Heisenberg category (with Samuel Nyobe Likeng, appendix with Christopher Ryba), Quantum Topology 12 (2021), no. 2, 211–242. (DOI, arXiv)
  17. String diagrams and categorification, Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification, Progress in Mathematics 337 (2021), 3–36. (DOI, arXiv)
  18. Heisenberg and Kac-Moody categorification (with Jonathan Brundan and Ben Webster), Selecta Mathematica 26 (2020), Paper No. 74, 62 pp. (DOI, arXiv)
  19. Quantum affine wreath algebras (with Daniele Rosso), Documenta Mathematica 25 (2020), 425–456. (DOI, arXiv)
  20. On the definition of quantum Heisenberg category (with Jonathan Brundan and Ben Webster), Algebra & Number Theory 14 (2020), no. 2, 275–321. (DOI, arXiv)
  21. Affine wreath product algebras, International Mathematics Research Notices IMRN 2020, no. 10, 2977–3041. (DOI, arXiv)
  22. Frobenius Heisenberg categorification, Algebraic Combinatorics 2 (2019), no. 5, 937–967. (DOI, arXiv)
  23. Invariant polynomials on truncated multicurrent algebras (with Tiago Macedo), Journal of Pure and Applied Algebra 223 (2019), no. 1, 349–368. (DOI, arXiv)
  24. Weyl modules for Lie superalgebras (with Lucas Calixto and Joel Lemay), Proceedings of the American Mathematical Society 147 (2019), no. 8, 3191–3207. (DOI, arXiv)
  25. Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification (with Marco Mackaay), Journal of Algebra 505 (2018), 150–193. (DOI, arXiv)
  26. An equivalence between truncations of categorified quantum groups and Heisenberg categories (with Hoel Queffelec and Oded Yacobi), Journal de l'École polytechnique — Mathématiques 5 (2018), 197–238. (DOI, arXiv)
  27. A graphical calculus for the Jack inner product on symmetric functions (with Anthony Licata and Daniele Rosso), Journal of Combinatorial Theory, Series A 155 (2018), 503–543. (DOI, arXiv)
  28. Nested Frobenius extensions of graded superrings (with Edward Poon), Involve 11 (2018), no. 3, 449–461. (DOI, arXiv)
  29. Heisenberg categorification, Research Notes, CMS Notes 49, no. 3 (June 2017), 16–17. (DOI)
  30. A general approach to Heisenberg categorification via wreath product algebras (with Daniele Rosso), Mathematische Zeitschrift 286 (2017), no. 1–2, 603–655. (DOI, arXiv)
  31. Equivariant map queer Lie superalgebras (with Lucas Calixto and Adriano Moura), Canadian Journal of Mathematics 68 (2016), 258–279. (DOI, arXiv)
  32. Twisted Frobenius extensions of graded superrings (with Jeffrey Pike), Algebras and Representation Theory 19 (2016), no. 1, 113–133. (DOI, arXiv)
  33. Towers of graded superalgebras categorify the twisted Heisenberg double (with Daniele Rosso), Journal of Pure and Applied Algebra 219 (2015), no. 11, 5040–5067. (DOI, arXiv)
  34. Twisted Heisenberg doubles (with Daniele Rosso), Communications in Mathematical Physics 337 (2015), no. 3, 1053–1076. (DOI, arXiv)
  35. Global Weyl modules for equivariant map algebras (with Ghislain Fourier and Nathan Manning), International Mathematics Research Notices IMRN 2015 (2015), no. 7, 1794–1847. (DOI, arXiv)
  36. Categorification and Heisenberg doubles arising from towers of algebras (with Oded Yacobi), Journal of Combinatorial Theory, Series A 129 (2015), 19–56. (DOI, arXiv)
  37. Extensions and block decompositions for finite-dimensional representations of equivariant map algebras (with Erhard Neher), Transformation Groups 20 (2015), 183–228. (DOI, arXiv)
  38. Introduction to categorification, CRM mini-course lecture notes, 2014. (DOI)
  39. Formal Hecke algebras and algebraic oriented cohomology theories (with José Malagón-Lopez, Alex Hoffnung, and Kirill Zainoulline), Selecta Mathematica 20 (2014), no. 4, 1213–1245. (DOI, arXiv). Erratum (DOI). Note: The arXiv version of the paper incorporates the erratum to the published version.
  40. Equivariant map superalgebras, Mathematische Zeitschrift 277 (2014), no. 1, 373–399. (DOI, arXiv)
  41. On the work of Igor Frenkel (with John Duncan, Pavel Etingof, Ivan Ip, Mikhail Khovanov, Matvei Libine, Anthony Licata, and Michael Schlosser), Perspectives in representation theory, 1–21, Contemporary Mathematics 610, Amer. Math. Soc., Providence, RI, 2014. (DOI)
  42. A survey of equivariant map algebras with open problems (with Erhard Neher), Recent developments in algebraic and combinatorial aspects of representation theory (Bangalore, India, 2010 and Riverside, CA, 2012), 165–182, Contemporary Mathematics 602, Amer. Math. Soc., Providence, RI, 2013. (DOI, arXiv)
  43. Hecke algebras, finite general linear groups, and Heisenberg categorification (with Anthony Licata), Quantum Topology 4 (2013), 125–185. (DOI, arXiv)
  44. Classification of irreducible quasifinite modules over map Virasoro algebras, Transformation Groups 17 (2012), no. 2, 547–570. (DOI, arXiv)
  45. A survey of Heisenberg categorification via graphical calculus (with Anthony Licata), Bulletin of the Institute of Mathematics Academia Sinica New Series 7 (2012), 291–321. (DOI, arXiv)
  46. Local Weyl modules for equivariant map algebras with free abelian group actions (with Ghislain Fourier, Tanusree Khandai, and Deniz Kus), Journal of Algebra 350 (2012), 386–404. (DOI, arXiv)
  47. Irreducible finite-dimensional representations of equivariant map algebras (with Erhard Neher and Prasad Senesi), Transactions of the American Mathematical Society 364 (2012), no. 5, 2619–2646. (DOI, arXiv)
  48. Geometric realizations of crystals, in Geometric representation theory and extended affine Lie algebras, Fields Institute Communications 59, Amer. Math. Soc., Providence, RI, 2011, 45–70. These are lecture notes from the 2009 University of Ottawa Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras. (arXiv)
  49. Quiver grassmannians, quiver varieties and the preprojective algebra (with Peter Tingley), Pacific Journal of Mathematics 251-2 (2011), 393–429. (DOI, arXiv). Erratum (DOI). Note: the arXiv version of the paper incorporates the erratum to the published version.
  50. Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves (with Anthony Licata), Selecta Mathematica 16 (2010), no. 16, 201–240. (DOI, arXiv)
  51. Braided and coboundary monoidal categories. Algebras, representations and applications (Maresias, Brazil, 2007), 229–251, Contemporary Mathematics 483, Amer. Math. Soc., Providence, RI, 2009. (DOI, arXiv)
  52. Crystals, quiver varieties and coboundary categories for Kac-Moody algebras, Advances in Mathematics 221 (2009), no. 1, 22–53. (DOI, arXiv)
  53. Quivers and the Euclidean group. Representation theory (Lhasa, China, 2007), 177–188, Contemporary Mathematics 478, Amer. Math. Soc., Providence, RI, 2007. (DOI, arXiv)
  54. Geometric and combinatorial realizations of crystals of enveloping algebras. Lie algebras, vertex operator algebras and their applications (Raleigh, NC, 2005), 221–232, Contemporary Mathematics 442, Amer. Math. Soc., Providence, RI, 2007. (DOI, arXiv)
  55. A geometric boson-fermion correspondence, C. R. Math. Rep. Acad. Sci. Canada 28 (2006), no. 3, 65–84. (DOI, arXiv)
  56. Finite-dimensional algebras and quivers, Encyclopedia of Mathematical Physics, eds. J.-P. Françoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006, volume 2, pages 313–320. (arXiv)
  57. On two geometric constructions of U(sln) and its representations, Journal of Algebra 305 (2006), no. 2, 664–686. (DOI, arXiv).
  58. Quiver varieties and Demazure modules, Mathematische Annalen. 335 (2006), no. 1, 31–46. (DOI, arXiv). Erratum (DOI). Note: the arXiv version of the paper incorporates the erratum to the published version.
  59. Geometric and combinatorial realizations of crystal graphs, Algebras and Representation Theory 9 (2006), no. 2, 161–199. (DOI, arXiv)
  60. A geometric realization of spin representations and Young diagrams from quiver varieties, Journal of Algebra 297 (2006), no. 1, 186–207. (DOI, arXiv)
  61. A geometric construction of crystal graphs using quiver varieties: extension to the non-simply laced case. Infinite-dimensional aspects of representation theory (Charlottesville, VA, 2004), 133–154, Contemporary Mathematics 392, Amer. Math. Soc., Providence, RI, 2005. (DOI, arXiv)
  62. Relations between algebraic and geometric constructions in representation theory, Yale University Dissertation, 2003. (pdf)
  63. Bases of representations of type A affine Lie algebras via quiver varieties and statistical mechanics (with Igor Frenkel), International Mathematics Research Notices IMRN 28 (2003), 1521–1547. (DOI, arXiv)
  64. Quiver varieties and fusion products for sl2 (with Olivier Schiffmann), Journal of Algebra 269 (2003), no. 2, 544–555. (DOI, arXiv)
  65. The tensor product of representations of Uq(sl2) via quivers, Advances in Mathematics 177 (2003), no. 2, 297–340. (DOI, arXiv)
  66. Magnon wave-function and impurity effects in S=1 antiferromagnetic chains: A large-n approach (with Ian Affleck), Physical Review B 59 (1999), 3635–3650. (DOI, arXiv)