2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
Horizons in Operator Algebras
Org: M. Ali Asadi-Vasfi (Purdue University), George Elliott (University of Toronto) and Viola Maria Grazia (Lakehead University Orillia)
[PDF]
Org: M. Ali Asadi-Vasfi (Purdue University), George Elliott (University of Toronto) and Viola Maria Grazia (Lakehead University Orillia)
[PDF]
- JANANAN ARULSEELAN, Iowa State University
- BRANIMIR CACIC, University of New Brunswick, Fredericton
Revisiting the differential topology of higher-dimensional noncommutative tori [PDF]
- BRANIMIR CACIC, University of New Brunswick, Fredericton
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The earliest results in noncommutative (NC) differential geometry à la Connes concern the differential topology of higher-dimensional NC tori. In this talk, I'll sketch how these results interface with recent progess in NC differential and Riemannian geometry. In particular, I'll sketch how Elliott's calculation of the diffeomorphism group of a Diophantine-irrational NC 2-torus generalizes to higher dimensions and how Rieffel–Schwarz and Li's classification of higher-dimensional NC tori up to complete Morita equivalence can be refined to classify NC Hermitian line bundles with unitary connection on totally irrational higher-dimensional NC tori up to gauge equivalence. This is partly based on joint work with T. Venkata Karthik.
- KEN DAVIDSON, U.Waterloo and U.Ottawa
Large Perturbations of Nest Algebras [PDF]
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Let $\mathcal{M}$ and $\mathcal{N}$ be nests on separable Hilbert space. If the two nest algebras are distance less than 1 ($d(\mathcal{T}(\mathcal{M}),\mathcal{T}(\mathcal{N})) < 1$), then the nests are distance less than 1 ($d(\mathcal{M},\mathcal{N})<1$). If the nests are distance less than 1 apart, then the nest algebras are similar, i.e. there is an invertible $S$ such that $S\mathcal{M} = \mathcal{N}$, so that $S \mathcal{T}(\mathcal{M})S^{-1} = \mathcal{T}(\mathcal{N})$. However there are examples of nests closer than 1 for which the nest algebras are distance 1 apart.
- ANDREW DEAN, Lakehead University
Classification problems concerning real structures and gradings [PDF]
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We shall give a survey and update on progress for problems
concerning classification of real structures and gradings on
$C^*$-algebras, and their associated range of invariant problems.
- REMUS FLORICEL, University of Regina
- SAEED GHASEMI, Lakehead University
- BRADD HART, McMaster University
- CRISTIAN IVANESCU, MacEwan University
Preservation of the Way-Below Relation Under Tensor Products [PDF]
- SAEED GHASEMI, Lakehead University
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We show that the way-below relation is preserved under tensor products. While completing this work, we became aware that, in the context of the Cuntz semigroup, an instance of this result was previously established by Antoine, Perera, and Thiel. We nevertheless present our proof here, as it provides a complementary approach and may offer additional insight into the behaviour of the way-below relation under tensorial constructions.
- DAVID KRIBS, University of Guelph
Operator Algebra Perspective on Entanglement-Assisted Quantum Codes [PDF]
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The idea of using entanglement as a resource in quantum computing and communication has been around for a long time. Two decades ago, 'entanglement-assisted' quantum codes were introduced in quantum error correction (EAQEC) as a resource for boosting transmission rates when a sender and receiver share pre-existing entanglement. Shortly thereafter, a pair of (not so clearly related I'd say) generalizations of EAQEC were formulated for 'subsystem codes' and for the classical enhancement of quantum code transmission. As it turns out, each of these three types of code can be viewed as special cases of a general framework for EA codes built on an operator algebra approach to quantum error correction. In addition to unifying these code types under a single umbrella, the resulting framework (EAOAQEC) yields new types of EA codes. In this talk, I'll give a brief introduction to entanglement-assisted codes, the EAOAQEC framework, and some of our results (time dependent). This talk is based on joint work with Serge Adonsou, Guillaume Dauphinais, Priya Nadkarni, and Michael Vasmer.
- HUAXIN LIN, Shanghai Institute for Mathematics and Interdisciplinary Sciences
Almost commuting selfadjoint operators and quantum mechanics [PDF]
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We show that Mumford's Approximately Macroscopically Unique (AMU) states exist
for quantum systems consisting of unbounded self-adjoint operators when the commutators are small.
In particular, AMU states always exist in position and momentum systems when the Planck constant
$|\hbar|$ is sufficiently small. However, we show that
these standard quantum mechanical systems are far away from classical mechanical (commutative) systems
even when
$|\hbar|\to 0.$
- AAREYAN MANZOOR, University Of Waterloo
There is a non-Connes embeddable Equivalence Relation [PDF]
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Connes embeddability of a group is a finite dimensional approximation property. It turns out this property depends only on the group von Neumann algebra. The property can be extended to all tracial von Neumann algebras. The fact that there is a von Neumann algebra without this property was proved in 2020 using the quantum complexity result MIP*=RE. It is still open for group von Neumann algebras. I will discuss the best-known partial result, which is that there is a group action without this property. In particular, this implies the negation to the Aldous-Lyons conjecture, a big problem in probability theory about finite approximability of a certain class of random graphs.
- PARTICK MELANSON, University of Regina
- MEHDI MORADI, University of Ottawa
- ZHUANG NIU, University of Wyoming
- DOLAPO OYETUNBI, University of Windsor
- EBRAHIM SAMEI, University of Saskatchewan
- CHRISTOPHER SCHAFHAUSER, University of Nebraska - Lincoln
KK-rigidity of simple nuclear C*-algebras [PDF]
- MEHDI MORADI, University of Ottawa
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A landmark result in C*-algebra theory is the classification of unital separable simple nuclear Z-stable C*-algebras satisfying the universal coefficient theorem (UCT) in terms of their K-theory and traces. I will discuss this result with a focus on the role of UCT. In the infinite setting, without the UCT, two unital Kirchberg algebras are isomorphic if and only they are KK-equivalent in a unit-preserving way. I’ll discuss some results along these lines in the finite case.
- THOMAS SINCLAIR, Purdue University
Computability of C*-norms [PDF]
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We will present joint work with Isaac Goldbring which combines techniques from continuous logic with the recent result MIP$^{\rm co}$ = coRE to answer a question of Fritz, Netzer, and Thom on the computability of the norm on $C^*(\mathbb F_2\times \mathbb F_2)$.
- CHARLES STARLING, Carleton University
Uniqueness theorems for combinatorial C*-algebras [PDF]
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Loosely speaking, a combinatorial C*-algebra is one defined in terms by generators and relations in some countable object, like a cancellative monoid, the paths in a directed graph, or the small category associated to a self-similar action. I will present uniqueness theorems akin to the classical Cuntz-Krieger uniqueness theorem, where injectivity of a *-homomorphism is equivalent to injectivity on a subalgebra generated by a subset of the generators.
- AARON TIKUISIS, University of Ottawa
- DAN URSU, York University
Non-conventional averaging in C*-algebras [PDF]
- DAN URSU, York University
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Several important averaging properties have shown up in the theory of operator algebras, most notably the Dixmier averaging property and its variants, which deals with convex averages of elements in some unitary orbit. In joint work with Matthew Kennedy, expanding upon the work of Magajna in the theory of C*-convex averages, we develop a strong new averaging property and separation theorem, and use it to characterize when the intermediate subalgebra structure of a crossed product is entirely canonical. Progress-permitting, we will also give a sneak peek at some preliminary results using these same averaging techniques applied to the ideal structure of crossed products.
- DILIAN YANG, University of Windsor