Ian Thompson, postdoc

Ian is from Canada and received his bachelor’s at the University of Manitoba in 2019. Afterwards, he enrolled in a master’s program at Manitoba, and subsequently transferred into a PhD. Ian completed his PhD at the University of Manitoba in 2024, under the supervision of Raphaël Clouâtre.

Ian's employment in Copenhagen is partly financed by the Department, partly by a fellowship offered by the Natural Sciences and Engineering Research Council of Canada.

Ian studies the structure of operator systems and non-self-adjoint operator algebras and their interactions with richer structures such as C*-algebras and von Neumann algebras. Often, operator algebraic statements are inspired by their function-theoretic counterparts. Indeed, this has brought forth the aphorisms of C*-algebras and von Neumann algebras being the study of noncommutative topology and measure theory, respectively.

Ian’s research thus far has lied under the umbrella of noncommutative convexity. This idea is just now reaching the frontiers of modern analysis, blending techniques from operator algebras with operator theory, and showcasing natural connections to semigroup dynamics, algebraic geometry, and complex function theory.

Ian’s primary contributions have been to one of the final conjectures of William Arveson. Arveson conjectured that the rigidity of an operator system inside a C*-algebra is encoded in an invariant inspired by classical convexity theory. The original statement was shown to be false, but Ian and his PhD supervisor have since shown that the core philosophy of Arveson's conjecture can still be witnessed.

At Copenhagen, Ian will be working with Søren Eilers and Magdalena Musat. He is excited to work with new collaborators and to increase his breadth of knowledge.

You can meet Ian in office 04.2.09