Investigating semi-Dirichlet matrix operator algebras - Phase 4
Preferred learners
- Edmonton, Alberta, Canada
- Academic experience or paid work
Categories
Skills
Project scope
- What is the main goal for this project?
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Operator algebras are collections of linear functions on geometric spaces of vectors called Hilbert spaces. Operator algebras represent collections of physical observables in quantum mechanics, and have also found application to many other mathematical fields. In the last 50 years, the study of operator algebras which are "non-selfadjoint", such as algebras of triangular matrices, has been especially fruitful. Of special interest in modern research-level mathematics are non-selfadjoint operator algebras which are "semi-Dirichlet".
In this project, a MacEwan undergraduate research assistant will instigate a theoretical and/or computer classification of those finite-dimensional operator algebras which are semi-Dirichlet. In the most basic cases, such algebras can be classified using directed graphs. A celebrated theorem of Burnside describes the structure of any finite-dimensional algebra, and a classification of the semi-Dirichlet property will combine graph theory and Burnside's Theorem.
By the end of this project, the student will produce an article suitable for publication in an undergraduate or research-level journal. This is new mathematical research carried out by an undergraduate researcher at MacEwan University, supervised by Drs. Adam Humeniuk and Chris Ramsey.
- What tasks will learners need to complete to achieve the project goal?
-
In the fourth phase, the student will finalize and submit for publication their research report.
- What is the main goal for this project?
-
Operator algebras are collections of linear functions on geometric spaces of vectors called Hilbert spaces. Operator algebras represent collections of physical observables in quantum mechanics, and have also found application to many other mathematical fields. In the last 50 years, the study of operator algebras which are "non-selfadjoint", such as algebras of triangular matrices, has been especially fruitful. Of special interest in modern research-level mathematics are non-selfadjoint operator algebras which are "semi-Dirichlet".
In this project, a MacEwan undergraduate research assistant will instigate a theoretical and/or computer classification of those finite-dimensional operator algebras which are semi-Dirichlet. In the most basic cases, such algebras can be classified using directed graphs. A celebrated theorem of Burnside describes the structure of any finite-dimensional algebra, and a classification of the semi-Dirichlet property will combine graph theory and Burnside's Theorem.
By the end of this project, the student will produce an article suitable for publication in an undergraduate or research-level journal. This is new mathematical research carried out by an undergraduate researcher at MacEwan University, supervised by Drs. Adam Humeniuk and Chris Ramsey.
- What tasks will learners need to complete to achieve the project goal?
-
In the fourth phase, the student will finalize and submit for publication their research report.
- How will you support learners in completing the project?
-
We will meet weekly throughout this project in-person or online, providing background information to the student and instruction on writing in LaTex (the mathematical typesetting language). Additionally, we will focus on skills development such as project management, searching for resources, programming, and publishing.
About the company
- https://www.macewan.ca/academics/academic-departments/mathematics-statistics/
- 0 - 1 employees
- Education
The Department of Mathematics and Statistics provides a vibrant and supportive home base for students who want to study mathematics and statistics. Our growing department is home to excellent scholars and has a deep commitment to student success, whether taking math as a requirement or as a pursuit of passion. Our faculty members are dedicated to providing an education that emphasizes the knowledge and broad analytical skills that are valuable in today’s world.
Beyond the classroom, our department organizes Torus Talks, a regular presentation series where faculty and students share insights into the uses and versatility of mathematics and statistics, and a Math Help Centre, where students can access additional support in mastering their course work.
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