## Publications and preprints

- On the definition of quantum Heisenberg category (with Jonathan Brundan and Ben Webster), 2018. (preprint)
- The degenerate Heisenberg category and its Grothendieck ring (with Jonathan Brundan and Ben Webster), 2018. (preprint)
- String diagrams and categorification, 2018. (preprint)
- Frobenius Heisenberg categorification, 2018. (preprint)
- Affine wreath product algebras,
*International Mathematics Research Notices IMRN*, to appear. (pdf, preprint) - Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification (with Marco Mackaay),
*Journal of Algebra***505**(2018), 150–193. (pdf, preprint) - 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), pp. 197–238. (pdf, preprint) - 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. (pdf, preprint) - Invariant polynomials on truncated multicurrent algebras (with Tiago Macedo),
*Journal of Pure and Applied Algebra*,**223**(2019), no. 1, 349–368. (pdf, preprint) - Nested Frobenius extensions of graded superrings (with Edward Poon),
*Involve***11**(2018), no. 3, 449–461. (pdf, preprint) - Heisenberg categorification,
*Research Notes, CMS Notes***49**, no. 3 (June 2017), pp. 16–17. (pdf) - A general approach to Heisenberg categorification via wreath product algebras (with Daniele Rosso),
*Mathematische Zeitschrift***286**(2017), no. 1–2, pp. 603–655. (pdf, preprint) - Weyl modules for Lie superalgebras (with Lucas Calixto and Joel Lemay),
*Proceedings of the American Mathematical Society*, to appear. (preprint) - Equivariant map queer Lie superalgebras (with Lucas Calixto and Adriano Moura),
*Canadian Journal of Mathematics***68**(2016), pp. 258–279. (pdf, preprint) - Twisted Frobenius extensions of graded superrings (with Jeffrey Pike),
*Algebras and Representation Theory***19**(2016), no. 1, pp. 113–133. (pdf, preprint) - Towers of graded superalgebras categorify the twisted Heisenberg double (with Daniele Rosso),
*Journal of Pure and Applied Algebra***219**(2015), no. 11, pp. 5040–5067. (pdf, preprint) - Twisted Heisenberg doubles (with Daniele Rosso),
*Communications in Mathematical Physics***337**(2015), no. 3, pp. 1053–1076. (pdf, preprint) - Global Weyl modules for equivariant map algebras (with Ghislain Fourier and Nathan Manning),
*International Mathematics Research Notices IMRN***2015**(2015), no. 7, pp. 1794–1847. (pdf, preprint) - Categorification and Heisenberg doubles arising from towers of algebras (with Oded Yacobi),
*Journal of Combinatorial Theory, Series A***129**(2015), pp. 19–56. (pdf, preprint) - Extensions and block decompositions for finite-dimensional representations of equivariant map algebras (with Erhard Neher),
*Transformation Groups***20**(2015), 183–228. (pdf, preprint) - Introduction to categorification, CRM mini-course lecture notes, 2014. (pdf)
- Formal Hecke algebras and algebraic oriented cohomology theories (with José Malagón-Lopez, Alex Hoffnung, and Kirill Zainoulline),
*Selecta Mathematica***20**(2014), no. 4, pp. 1213–1245. (pdf, preprint). Erratum (pdf).*Note:*The preprint version of the paper incorporates the erratum to the published version. - Equivariant map superalgebras,
*Mathematische Zeitschrift***277**(2014), no. 1, pp. 373–399. (pdf, preprint) - 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. (pdf) - 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. (pdf, preprint) - Hecke algebras, finite general linear groups, and Heisenberg categorification (with Anthony Licata),
*Quantum Topology***4**(2013), 125–185. (pdf, preprint) - Classification of irreducible quasifinite modules over map Virasoro algebras,
*Transformation Groups***17**(2012), no. 2, pp. 547–570. (pdf, preprint) - A survey of Heisenberg categorification via graphical calculus (with Anthony Licata),
*Bulletin of the Institute of Mathematics Academia Sinica New Series***7**(2012), pp. 291–321. (pdf, preprint) - 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. (pdf, preprint) - 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. (pdf, preprint) - Geometric realizations of crystals, in Geometric representation theory and extended affine Lie algebras, Fields Institute Communications
**59**, Amer. Math. Soc., Providence, RI, 2011, pp. 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. (preprint) - Quiver grassmannians, quiver varieties and the preprojective algebra (with Peter Tingley),
*Pacific Journal of Mathematics***251-2**(2011), 393–429. (pdf, preprint). Erratum (pdf).*Note:*the preprint version of the paper incorporates the erratum to the published version. - Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves (with Anthony Licata),
*Selecta Mathematica***16**(2010), no. 16, 201–240. (pdf, preprint) - Braided and coboundary monoidal categories.
*Algebras, representations and applications (Maresias, Brazil, 2007)*, 229–251, Contemporary Mathematics**483**, Amer. Math. Soc., Providence, RI, 2009. (pdf, preprint) - Crystals, quiver varieties and coboundary categories for Kac-Moody algebras,
*Advances in Mathematics***221**(2009), no. 1, 22–53. (pdf, preprint) - Quivers and the Euclidean group.
*Representation theory (Lhasa, China, 2007)*, 177–188, Contemporary Mathematics**478**, Amer. Math. Soc., Providence, RI, 2007. (pdf, preprint) - 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. (pdf, preprint) - A geometric boson-fermion correspondence,
*C. R. Math. Rep. Acad. Sci. Canada***28**(2006), no. 3, 65–84. (pdf, preprint) - 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. (preprint) - On two geometric constructions of U(sl
_{n}) and its representations,*Journal of Algebra***305**(2006), no. 2, 664–686. (pdf, preprint). - Quiver varieties and Demazure modules,
*Mathematische Annalen.***335**(2006), no. 1, 31–46. (pdf, preprint). Erratum (pdf).*Note:*the preprint version of the paper incorporates the erratum to the published version. - Geometric and combinatorial realizations of crystal graphs,
*Algebras and Representation Theory***9**(2006), no. 2, 161–199. (pdf, preprint) - A geometric realization of spin representations and Young diagrams from quiver varieties,
*Journal of Algebra***297**(2006), no. 1, 186–207. (pdf, preprint) - 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. (pdf, preprint) - Relations between algebraic and geometric constructions in representation theory, Yale University Dissertation, 2003. (pdf)
- 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. (pdf, preprint) - Quiver varieties and fusion products for sl
_{2}(with Olivier Schiffmann),*Journal of Algebra***269**(2003), no. 2, 544–555. (pdf, preprint) - The tensor product of representations of U
_{q}(sl_{2}) via quivers,*Advances in Mathematics***177**(2003), no. 2, 297–340. (pdf, preprint) - 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. (pdf, preprint)

## Editorial Work

I am currently an Associate Editor of the Canadian Journal of Mathematics, the Canadian Mathematical Bulletin, and Algebras and Representation Theory. In addition, I have co-edited the following volumes.

- Perspectives in Representation Theory (eds. with Pavel Etingof and Mikhail Khovanov), Contemporary Mathematics
**610**, Amer. Math. Soc., Providence, RI, 2014. - 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. - Categorification in Representation Theory (eds. with Aaron Lauda and Anthony Licata), International Journal of Mathematics and Mathematical Sciences
**2010**, Hindawi, 2010.