Upcoming Conferences, Workshops Etc.

Below I will indicate upcoming conferences that I will be attending.

• November 30-December 5: Operator Algebraic Quantum Groups, BIRS.

Preprints and Publications

My research interests are on things having to do with (quantum) groups, abstract harmonic analysis, operator algebras, and closely related fields. More particularly, I'm interested in studying the operator algebras associated to (quantum) groups in relation to the intrinsic properties / representation theory of the given (quantum) groups and their (noncommutative) dynamics (e.g. actions on compact spaces, C*-algebras, operator spaces, etc).

Preprints:

• (with R. Vergnioux) $C^*$-simplicity and Boundary Actions of Discrete Quantum Groups, arXiv:2411.05178 - arXiv 

• (with T. de Laat, E. Samei, and M. Wiersma) Entropies and Poisson Boundaries of Random Walks on Groups with Rapid Decay, arXiv:2410.19689 - arXiv 

• (with L. Vainerman) Fusion Modules and Amenability of Coideals of Compact and Discrete Quantum Groups,  arXiv:2308.01656 - arXiv 

Publications:

• Tracial States and $\mathbb{G}$-Invariant States of Discrete Quantum Groups, Studia Mathematica, Vol: 279, No: 1, (2024), 71-96 - arXiv  

• (with F. Khosravi) Topological Boundaries of Representations and Coideals, Advances in Mathematics, Vol: 452, No. 109830 (2024) - arXiv 

• On Amenable and Coamenable Coideals, Journal of Noncommutative Geometry, Vol: 18, No: 3 (2024), 1129–1163 - arXiv

• On Ideals of $L^1$–algebras of Compact Quantum Groups, International Journal of Mathematics, Vol: 22, No: 12, 2250074  (2022) - arXiv 

Comments on Articles

• On Ideals of $L^1$–algebras of Compact Quantum Groups. A typo was kindly pointed out to me by Matthew Daws. In Section 3.3, the definition of condition (H) of an element $x\in L^\infty(\G)$ should be replaced with "$x \in \overline{x\conv L^1(\G)}^{wk*}$". Note that the unitary antipode can be used to prove every $x$ has condition (H) in this sense iff every $x$ has condition (H) in the sense as in the article.

• Topological Boundaries of Representations and Coideals. A minor comment was kindly give to me by Joeri de Ro. In the statement of Theorem 6.1, the assumption of injectivity of a vN-algebraic coideal of a DQG is given. Note, however, that coideals of DQGs are always injective because they are direct products of matrix algebras (see [15]).

Additional Roles

As a known Indigenous mathematician of North America, I have a profile here. In that regard, I'm a member of the Fort Albany First Nation and was born and raised off-reserve in Timmins, Ontario. My paternal side is Cree, with my father being from Moosonee, my grandfather's side originating in Fort Albany and my grandmother's side originating in Waskaganish. My maternal side is Danish and Irish, with my grandfather having been from Denmark and my grandmother having been of Irish descent.