Ian Thompson

E-mail: thompsoi "at" myumanitoba "dot" ca

I am a Ph.D. candidate at the University of Manitoba who is studying operator algebras and operator theory with Raphaël Clouâtre. My current research projects focus on non-commutative interpretations of the Choquet boundary. If you are interested in projects of this nature or a related topic, feel free to contact me.

Alongside these projects, I work as a graduate supervisor for Robert Craigen (previously, Vitalii Akimenko, Richard Mikaël Slevinsky and Joshua Males) as a part of the Manitoba eXperimental Mathematics Laboratory. An online variation, VXML, is offered by the Pacific Institute for the Mathematical Sciences. During the Summer 2022 term, I took an academic leave to work as a data scientist at Quantolio.

Publications

(with Jashan Bal, Fern Haraldson, and Joshua Males) Jensen polynomials associated with Wright's circle method: hyperbolicity and Turán inequalities.
Submitted for publication, arXiv.
An approximate unique extension property for completely positive maps.
J. Funct. Anal. 286 (2024), no. 1, 110193 arXiv, DOI.
(with Idrissa Ba and Adam Clay) The number of locally invariant orderings of a group.
J. Group Theory 26 (2023), no. 5, 1003-1021 arXiv, DOI.
(with Raphaël Clouâtre) Minimal boundaries for operator algebras.
Trans. Amer. Math. Soc. B 10 (2023), no. 24, 807-832 arXiv, DOI.
Maximal C*-covers and residual finite-dimensionality.
J. Math. Anal. Appl. 514 (2022), no. 1, 126277, arXiv, DOI.
(with Raphaël Clouâtre) Finite-dimensionality in the non-commutative Choquet boundary: peaking phenomena and C*-liminality.
Int. Math. Res. Not. IMRN (2022), no. 20, 16046-16093, arXiv, DOI.

Teaching

In the 2021-2022 academic year, I was teaching MATH 1500 (Introduction to Calculus) at the University of Manitoba.