Adam Humeniuk

Pronouns: (he/him/his)

ahumeniuk (at) mtroyal (dot) ca

adam.humeniuk (at) gmail (dot) com

ORCiD

Assistant Professor - Mount Royal University, 2023-

Postdoctoral Fellow - MacEwan University, 2022-2023

Term Instructor - University of Alberta, 2022

PhD - Pure Mathematics University of Waterloo, 2018-2022.

(Thesis Title: Dilation methods in semigroup dynamics and noncommutative convexity.)

MMath - Pure Mathematics: University of Waterloo, 2017-2018.

BSc. Hons. - Pure Mathematics (After Degree): University of Calgary, 2015-2017.

BSc. Hons. - Physics: University of Calgary, 2011-2015.

About Me

I am an Assistant Professor in Mathematics at Mount Royal University, in Calgary, Alberta. I completed my PhD at the University of Waterloo in July 2022. I'm originally from Calgary, Alberta.

In my free time, I am passionate about strength training, rock climbing, hiking, music, and cooking.

Research

I enjoy researching operator algebras and operator theory, and their application to dynamics and convexity. I am interested in the C*-covers and C*-envelopes of non-selfadjoint operator algebras, including those related to semigroup dynamics. I am also researching noncommutative (AKA matrix) convexity and its dual relationship to the category of operator systems.

Publications

A. Humeniuk, M. Kennedy, and N. Manor (2023), An extension property for noncommutative convex sets and duality for operator systems, arXiv Preprint arxiv: 2312.04791. arXiv
A. Humeniuk, E. G. Katsoulis, and C. Ramsey (2023), Crossed products and C*-covers of semi-Dirichlet operator algebras, arXiv Preprint arXiv:2309.16130. arXiv
A. Humeniuk and C. Ramsey (2023), The Lattice of C*-covers of an operator algebra, arXiv Preprint arXiv:2304.02783. arXiv
A. Humeniuk (2021), Jensen’s Inequality for Separately Convex Noncommutative Functions, IMRN, 2023(2), 998-1035. DOI, arXiv
A. Humeniuk (2020), C*-envelopes of semicrossed products by lattice ordered abelian semigroups. J. Funct. Anal., 279(9), 108731 (2020). DOI, arXiv
M. Khazali, H. W. Lau, A. Humeniuk, and C. Simon (2016). Large energy superpositions via Rydberg dressing. Phys. Rev. A , 94(2), 023408. DOI, arXiv

Here is a link to my PhD Thesis Dilation methods in semigroup dynamics and noncommutative convexity (2022).

Here is a link to my Master's project Existence of the C*-Envelope of an Operator System (2018), which is a tour of the different proofs of existence of the C*-envelope of an operator system.

Courses Taught

MATH 2200 - Calculus for Scientists II, Mount Royal University, Winter 2024.
MATH 1203 - Linear Algebra for Scientists and Engineers, Mount Royal University, Winter 2024.
MATH 1200 - Calculus for Scientists I, Mount Royal University, Fall 2023.
MATH 225 - Linear Algebra II, University of Alberta, Fall 2022
MATH 135 - Algebra for Honours Mathematics, University of Waterloo, Fall 2021.

Students Supervised

Justin Rumball, Spring-Summer 2023
- Undergraduate summer project supported by Riipen LevelUP.
- Jointly Supervised with Dr. Chris Ramsey.
Orion Sehn, Fall 2022
- MATH 498 - Advanced Independent Study in Mathematics.
- Jointly Supervised with Dr. Chris Ramsey.