Overview

I am an algebraist working in an area of mathematics called Representation Theory which, broadly speaking, seeks to understand complicated abstract algebraic structures by how they "act" on concrete linear spaces, where the full force of linear algebra can be applied. In my work, the relevant abstract structures are quantum groups and quantum symmetric pairs. Roughly speaking, these arise when one "deforms" classical algebraic structures like Lie groups and Lie algebras. The representation theory of these quantum algebras frequently intertwines algebra, mathematical physics and geometry, and these interactions inspire a wealth of interesting problems and mathematics. For more information specific to my work, please see the Publications section below. 

Prospective Students

If you are an undergraduate student at the University of Saskatchewan interested in pursuing summer research opportunities in algebra, please don't hesitate to get in touch with me by email.

If you are a student interested in pursuing master's or doctoral studies in representation theory and have questions about my research area or potential opportunities, please contact me by email. For general information about application procedures, please see the following pages:

Preprints

  1. The R-matrix of the affine Yangian, with Andrea Appel and Sachin Gautam. Submitted for publication. pdf

Publications

  1. Braid group actions, Baxter polynomials, and affine quantum groups, with Noah Friesen and Alex Weekes. Transactions of the American Mathematical Society. Published online 2024:1-44. doi:10.1090/tran/9279. pdf
  2. The R-matrix presentation for the rational form of a quantized enveloping algebra, with Matthew Rupert. Journal of Algebra 647 (2024), 28-71. pdf
  3. The restricted quantum double of the Yangian. Canadian Journal of Mathematics. Published online 2024:1-76. doi:10.4153/S0008414X24000142. pdf
  4. The R-matrix formalism for quantized enveloping algebras, with Sachin Gautam and Matthew Rupert. To appear in Annales de l'Institut Fourier. pdf
  5. On a conjecture of Khoroshkin and Tolstoy, with Andrea Appel and Sachin Gautam. International Mathematics Research Notices 2023, no. 24, 21690–21706. pdf
  6. Poles of finite-dimensional representations of Yangians, with Sachin Gautam. Selecta Mathematica (N.S.) 29 (2023), no. 1, Paper No. 13, 68 pp. pdf
  7. The formal shift operator on the Yangian double. International Mathematics Research Notices 2022, no. 14, 10952–11010. pdf
  8. The meromorphic R-matrix of the Yangian, with Sachin Gautam and Valerio Toledano Laredo. In: Representation Theory, Mathematical Physics, and Integrable Systems (special volume in honour of the 60th birthday of Kolya Reshetikhin). Progress in Mathematics 340 (2021). pdf
  9. Vertex Representations for Yangians of Kac-Moody algebras, with Nicolas Guay and Vidas Regelskis. Journal de l'École polytechnique — Mathématiques 6 (2019), 665-706. pdf
  10. Coproduct for Yangians of affine Kac-Moody algebras, with Nicolas Guay and Hiraku Nakajima. Advances in Mathematics 338 (2018), 865-911. pdf
  11. Representations of twisted Yangians of types B, C, D: II, with Nicolas Guay and Vidas Regelskis. Transformation Groups 24 (2019), 1015-1066. pdf
  12. The R-matrix presentation for the Yangian of a simple Lie algebra. Communications in Mathematical Physics 363 (2018), no. 1, 289-332. pdf
  13. Equivalences between three presentations of orthogonal and symplectic Yangians, with Nicolas Guay and Vidas Regelskis. Letters in Mathematical Physics 109 (2019), no. 2, 327-379. pdf
  14. Representations of twisted Yangians of types B, C, D: I, with Nicolas Guay and Vidas Regelskis. Selecta Mathematica (N.S.) 23 (2017), no. 3, 2071-2156. pdf
  15. Twisted Yangians of small rank, with Nicolas Guay and Vidas Regelskis. Journal of Mathematical Physics 57 (2016), no. 4, 041703, 28 pp. pdf

Other

  1. Representations of Twisted Yangians of Types B, C and D, PhD thesis completed at the University of Alberta (2019). pdf