Conference for the Operator-Minded Philomathic Youth (COMPhY)
COMPhY is a two-day conference aimed at early career researchers interested in operator algebras. There will be two mini-courses delivered by established researchers in the area. In addition, there will be a career discussion session and time will be allocated for interested participants to give lightning talks advertising their research.
COMPhY 2025 will take place May 24-25, 2025 at the University of Waterloo in affiliation with COSy (Canadian Operator Symposium).
Please find more information below.
Mini-Courses
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University of Southern Denmark
When is an operator system a C*-algebra?
Abstract: When is an operator system a C*-algebra, and more importantly how can we verify it? (Partial) answers come via injectivity, noncommutative Choquet theory, and, more recently, inductive sequences of matrix algebras. Here by inductive sequence, we mean sequences of matrix algebras connected by completely positive maps. In 1997, Blackadar and Kirchberg investigated such systems and found sufficient conditions ensuring the limit is a C*-algebra-- a nuclear quasidiagonal one at that (motivating their famous quasidiagonality conjecture). Their constructions have recently been generalized in a number of settings, one of which allows for a complete characterization of when nuclear operator systems are C*-algebras in terms of their matrix approximations.
I will describe the theory around these topics to date, stopping and perhaps detouring at substantial theorems and constructions along the way.
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Noncommutative convexity and boundaries for operator systems
Abstract: In 1969, Arveson envisioned an ambitious program aiming to construct, for a given operator system, a noncommutative analogue of the Choquet boundary from classical convexity theory. This vision was eventually fully realized 45 years later, culminating in a theorem of Davidson and Kennedy on boundary representations. Even today, there remains some mysteries surrounding Arveson’s ideas, such as the important question of characterizing hyperrigid operator systems.
I will give the necessary background to understand and appreciate all these developments, as well as their connections to noncommutative convexity theory. No prior specialized knowledge on these topics will be assumed.
Schedule
The main events of the conference will take place on the Saturday and Sunday before COSy. Detailed schedule to come.
Registration
To register for COMPhY, please use the registration form for COSy and check the box for COMPhY. We will reach out to participants to sign up for lightning talks. We invite those interested in giving a longer talk to submit an abstract for a contributed talk at COSy by checking the appropriate box in the registration form.
Organizers: Thomas Bray, Larissa Kroell, and Erik Séguin
If you have any questions, please reach out to COMPhY2025@gmail.com