Ian Thompson

E-mail: ian "at" math.ku.dk
Office: HCØ 04.2.09

I am an NSERC Postdoctoral Fellow at the University of Copenhagen studying operator algebras and operator theory with Søren Eilers and Magdalena Musat. In this role, I am co-organizing the Groups and Operator Algebras Seminar.

In 2024, I completed my Ph.D. at the University of Manitoba under the supervision of Raphaël Clouâtre. My past work has focused on interactions between operator systems and C*-algebras, as well as their interactions with other fields.

Publications

(with Adam Dor-On) Obstructions to the full Hao-Ng isomorphism, arXiv.
Remark: Mukohara and Suzuki have independently obtained another counterexample to the full Hao-Ng isomorphism.
On the universal commuting dilation constant.
Submitted for publication, arXiv.
(with Adam Humeniuk and Christopher Ramsey) Couniversality for C*-algebras of residually finite-dimensional operator algebras.
Submitted for publication, arXiv.
(with Adam Dor-On) The Hao-Ng isomorphism theorem for reduced crossed products.
Submitted for publication, arXiv.
(with Alexandru Chirvasitu) Local presentability and monadicity of forgetful functors for operator algebraic categories.
J. Pure. Appl. Algebra 230 (2026), no.9, 108355, arXiv, DOI.
(with Raphaël Clouâtre) Rigidity of operator systems: tight extensions and noncommutative measurable structures.
In revision at Journal of the European Mathematical Society, arXiv.
(with Jashan Bal, Fern Haraldson, and Joshua Males) Jensen polynomials associated with Wright's circle method: hyperbolicity and Turán inequalities.
Integers 25 (2025), no. 36, arXiv, DOI.
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

Instructor:

Stability and Lifting in Operator Algebras (University of Copenhagen, joint with Søren Eilers)
Introduction to Calculus (x2, University of Manitoba)

Mentorship and Supervision

Master's Theses:

Julius Beck Schwartz: Rigidity properties for operator systems (2026)

Bachelor's Theses:

Ittai Turin: Dilations of probability measures on compact convex sets (2026)
Neo Strecker: Reformulations of the Kadison-Singer problem (2025)
William Gabel: Combinatorial and convex geometries of doubly stochastic matrices (2025)

Bachelor's Projects:

(with Robert Craigen) Nolan Coughlan: Elementary synthetic orthogonality theory (2024)
(with Vitalii Akimenko) Gurdit Singh, Sahilpreet Singh Sidhu: Stability analysis of an age-structured model of cancer cells (2023)
(with Richard Mikaël Slevinsky) Pedro Lopez Gascon, Adam Wieler: Modification algorithms for Sobolev orthogonal polynomials (2023)
(with Joshua Males) Jashan Bal, Fern Haraldson: Jensen polynomials associated with Wright’s circle method (2022)

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