### 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:

- https://artsandscience.usask.ca/math/graduates/procedure.php
- https://artsandscience.usask.ca/math/graduates/programs.php

### Preprints

### Publications

*The R-matrix presentation for the rational form of a quantized enveloping algebra*, with Matthew Rupert. Journal of Algebra**647**(2024), 28-71. pdf*The restricted quantum double of the Yangian.*Published online 2024:1-76. doi:10.4153/S0008414X24000142. pdf*Canadian Journal of Mathematics*.*The R-matrix formalism for quantized enveloping algebras*, with Sachin Gautam and Matthew Rupert. To appear in Annales de l'Institut Fourier. pdf*On a conjecture of Khoroshkin and Tolstoy,*with Andrea Appel and Sachin Gautam. International Mathematics Research Notices**2023**, no. 24, 21690–21706. pdf*Poles of finite-dimensional representations of Yangians*, with Sachin Gautam. Selecta Mathematica (N.S.)**29**(2023), no. 1, Paper No. 13, 68 pp. pdf*The formal shift operator on the Yangian double*. International Mathematics Research Notices**2022**, no. 14, 10952–11010. pdf*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*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*Coproduct for Yangians of affine Kac-Moody algebras*, with Nicolas Guay and Hiraku Nakajima. Advances in Mathematics**338**(2018), 865-911. pdf*Representations of twisted Yangians of types B, C, D: II*, with Nicolas Guay and Vidas Regelskis. Transformation Groups**24**(2019), 1015-1066. pdf*The R-matrix presentation for the Yangian of a simple Lie algebra*. Communications in Mathematical Physics**363**(2018), no. 1, 289-332. pdf*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*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*Twisted Yangians of small rank*, with Nicolas Guay and Vidas Regelskis. Journal of Mathematical Physics**57**(2016), no. 4, 041703, 28 pp. pdf

### Other

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