
THEMATIC PROGRAMS 

July 17, 2024  
Thematic Program on Operator AlgebrasOntario NonCommutative Geometry and Operator Algebras Seminars

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For more information about this program please contact George
Elliott
UPCOMING SEMINARS (for
200809 Seminars after July 1 )
February 21, March 20, April 17, May 15 revised start time 3:00
pm
July 3 Nadish de Silva July 1 Canada Day No seminar June 26 Leonel Robert June 24 Aaron Tikuisis June 19 Kevin Teh June 17 Aaron Tikuisis June 12 Alin Ciuperca June 10 Greg Maloney June 5 Greg Maloney June 3 Greg Maloney May 13 Alan Ciuperca May 8 2:10pm, Rm 210 Greg Maloney May 6, 2:10pm, Rm 210 Greg Maloney April 17 Aaron Tikuisis April 15 Greg Maloney April 5 John Phillips, University of Victoria
An Index Theory for Certain Gauge Invariant KMS Weights on C*algebras.April 1 Aaron Tikuisis Mar. 20 Asger Tornquist and Roman Sasyk
On the (non)classification of factors in vN algebrasMar. 18 Fernando Mortari Mar. 13 Trieu Le Mar. 11 Leonel Robert Mar. 6
Alin Ciuperca Mar. 4 Leonel Robert Feb. 28 Takeshi Katsura
Nonseparable UHF algebrasFeb. 26 Maria Grazia Viola Feb. 19 Sergio Doplicher, University of Rome 1
Quantum Spacetime and Noncommutative GeometryAbstract: We investigate the interplay between the universal differential calculus and other known algebraic structures, like Hochschild boundary on one side, and the C*structure on the other.The latter provides natural norms one can evaluate on forms; we will discuss a relevant application in the case of the algebra of Quantum Spacetime, that will be discussed and physically motivated.One finds that, while the Algebra itself is fully translation and Lorentz invariant, the four dimensional Euclidean distance is a positive operator bounded below by a constant of order one (in Planck units); the area operator and the four volume operator are normal operators, the latter being a Lorentz invariant operator with pure point spectrum, whose moduli are also bounded below by a constant of order one. While the spectrum of the 3 volume operator includes zero. These findings are in perfect agreement with the physical intuition suggested by the Spacetime Uncertainty Relations which are implemented by the Algebra of Quantum Spacetime. The formulations of interactions between quantum fields on Quantum Spacetime will be discussed. The various approaches to interactions, equivalent to one another on the Minkowski background, yield to different schemes on Quantum Spacetime, with the common feature of a breakdown of Lorentz invariance due to interactions. In particular one of these schemes will be discussed and motivated, which leads to fully UltravioletFinite theories.
We will conclude with remarks on the fact that, in presence of Gravity, the commutators of the coordinates might in turn depend on the quantum fields, giving rise to a quantum texture where fields and spacetime coordinates cannot be separated.
Feb. 14 Takeshi Katsura
Cocycle crossed productsFeb. 12 Leonel Robert Feb. 7 Sniggy Mahanta On a moduli space problem in Noncommutative Geometry
Feb. 5 Greg Maloney Jan. 24 Luis Santiago Jan. 22 Kris Coward Jan. 17 Trieu Le Jan. 15 Leonel Robert Jan. 10
Alin Ciuperca Jan. 7 Luis Santiago Dec. 6
Yasuhiko Sato
An application of the EvansKishimoto intertwining argument
I will explain about an existence of an extension of automorphisms on unital Kirchberg algebras. This theorem is an application of the EvansKishimoto intertwining argument. So I will explain about the homotopy lemma for the stability and proof of this theorem.
Huaxin Lin, University of Oregon
Approximate unitary equivalence in simple C*algebras of tracial rank one
It will be an informal report. We will present a theorem which tells us when two monomorphisms from some AHalgebra into a unital simple C*algebra of tracial rank one are approximate unitarily equivalent.
We will revisit approximately multiplicative completely positive linear contractions from C(X) into a matrix algebra. We will discuss the problem when they are close to a homomorphism. Then we will discuss approximately multiplicative completely positive linear contractions from
C(X) into an interval algebra. Perhaps we will also discuss when the general cases can be obtained from these two cases.Dec. 4
David Kyed (Copenhagen University)
L^2Betti numbers for compact quantum groups
L^2Betti numbers have proved themselves important within the theory of discrete groups and it is therefore reasonable to ask for an extension of this concept to the world of quantum groups. I will discuss one natural way to obtain such an extension for compact quantum groups with tracial Haar state, and thereafter discuss computational results and an extension of classical result (about L^2Betti numbers for amenable groups) to the quantum setting.Nov. 29
Toshihiko Masuda
Classification of minimal actions of a compact Kac algebras with amenable dual on the AFD factor of type II_1
I will explain the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group on the AFD factor of type II_1. This is a joint work with R. Tomatsu.
Takeshi Katsura
The EvansKishimoto intertwining argument
I present the classification result of Z^2actions on UHF algebras which was obtained by joint work with Hiroki Matui. I talk about the EvansKishimoto intertwining argument, which is one of the ingredient of the proof, with emphasis on possibility (or impossibility) of generalizing our argument to more general groups and algebras.Nov. 27
Francesc Perera (Universitat Autonoma de Barcelona)
Purely infinite corona algebras.Nov. 22
Aidan Sims, University of Wollongong, Australia
Compactly aligned product systems and CuntzNicaPimsner algebras
In his seminal paper, Pimsner introduced a class of C*algebras O_X associated to C*correspondences X over A. Now known as CuntzPimsner algebras, these C*algebras simultaneously generalise CuntzKrieger algebras and crossed products by Z. In Pimsner's
theory, if a in A satisfies a \cdot x = 0 for all x in X, then the canonical image of a in O_X is itself equal to zero; a situation which is at odds with the point of view suggested by graph algebras as generalised CuntzKrieger algebras. Recently, Katsura has modified Pimsner's construction to remedy this issue, and used the resulting C*algebras to define and analyse his topological graph C^*algebras. Discrete product systems X of C*correspondences and associated C*algebras O_X were introduced by Fowler with a view to simultaneously generalising Pimsner's construction and work of Nica and others on Toeplitz algebras associated to quasilattice ordered groups (G,P). Fowler's construction has the same drawbacks as Pimsner's when nonzero elements of A act trivially on the left of some fibres of X, but the example of higherrank graph C*algebras show that more subtle issues may arise even when each nonzero a acts nontrivially on each fibre. In this talk I shall show how to modify Fowler's construction to circumvent these issues. I will indicate how the resulting CuntzNicaPimsner algebras simultaneously generalise Katsura's O_X, higherrank graph C^*algebras, and Crisp and Laca's boundaryquotient algebras. This talk is based on joint work with Yeend, and with Carlsen, Larsen and Vittadello.
Gunnar Restorff, University of Copenhagen
Computing Kirchberg's Idealrelated KKtheory
KKtheory is an important tool in the theory of classification of C*algebra. Kirchberg's development of an idealrelated version of KKtheory has been shown to be important for the classification of (nonsimple) purely infinite C*algebras. To obtain a univariant (classifying) functor instead of using the bivariant KKfunctor, one needs some results along the lines of Rosenberg and Schochet's UCT and Dadarlat and Loring's UMCT. Even though some progress has been made, this has not at all been solved yet. I will start out by introducing the usual UCT and UMCT. Then I will focus on the case where the specified idealstructure is just a single ideal, and talk about a UCT by Bonkat and some related problems that arise in this case. This is joint work with Sï¿½ren Eilers and Efren Ruiz.Nov. 20
Robin Deeley (University of Victoria)
The Orbit Operator
Given a bounded linear operator and a vector in a Hilbert space on which it acts, we associate a linear map which we call the orbit operator. The orbit operator has trivial kernel if and only if the vector is a cyclic vector of the original operator. We discuss the connections between the orbit operator and invariant subspaces and the differing behaviour of the orbit operators associated with contractions and strict
contractions.Nov. 8
Luis Santiago
Extended traces on a C*algebra and the Cuntz semigroupOct. 25
Ivan Dynov (Max Planck Institute for Mathematics)
The type III_1 factor generated by the regular representations of the infinitedimensional group $(B_0)^Z$.
Martin Mathieu (Queen's University Belfast)
Spectral characterizations of Jordan homomorphisms
I will try to explain and motivate a problem on operators on II_1 factors that I am currently thinking about.Tuesday,
23 October 2007,
Ilan Hirshberg (Ben Gurion University)
C(X)algebras and strongly selfabsorbing C*algebra
Let X be a finite dimensional space, and A a separable C(X)algebra. I'll discuss the following result: if D is a K_1injective strongly selfabsorbing C*algebra, and each fiber A_x of the C(X)algebra is Dabsorbing, then A is Dabsorbing. This is joint work with Mikael Rordam and Wilhelm Winter.Oct. 18
Ilijas Farah (York University)
All automorphisms of the Calkin algebra are inner
Phillips and Weaver have proved that the Continuum Hypothesis implies the existence of an outer automorphism of the Calkin algebra. On the other hand, Todorcevic's Open Colouring Axiom, OCA, implies that all the automorphisms of the Calkin algebra are inner. I will discuss OCA and present key parts of the proof of the latter theorem. No knowledge of the set theory is required.
Marius Dadarlat (Purdue University)
Trivialization of continuous fields of C*algebras with strongly selfabsorbing fibers
Let A be a separable unital continuous field over a finite dimensional compact metric space X. Suppose that each fibre of A is
isomorphic to the same strongly selfabsorbing and K1injective C*algebra D. Then A is trivial field, i.e., A is isomorphic to C(X, D). The class of strongly selfabsorbing C*algebras was introduced by Winter and Toms. The only known examples are the UHF algebras of infinite type, the Cuntz algebras O(2) and O(infinity), the JiangSu algebra and tensor products of O(infinity) with UHF algebras of infinite type. All these examples are K1injective.Tuesday,
16 October 2007,
Bruce Blackadar (University of Nevada, Reno)
Nonstable Ktheory for properly infinite C*algebras and unital free products.Oct. 11
Snigdhayan Mahanta (Max Planck Institute for Mathematics)
Holomorphic vector bundles over noncommutative tori
The category of the holomorphic vector bundles over noncommutative 2tori will be discussed. Given any irrational $\theta$, a faithful exact functor from the category of finite dimensional representations of $\mathbb{Z} + \theta\mathbb{Z}$ to the category of holomorphic vector bundles over the noncommutative torus $\mathbb{T}_\theta$ will be constructed. Some homotopy theoretic consequences will be discussed. The flavour of the talk will be mostly algebraic (and geometric), rather than operator algebraic. This is a joint work with W. D. van Suijlekom.
Mike Whittaker (University of Victoria)
C*algebras from Tilings and Infinite Rotational Symmetry
Tilings with infinite rotational symmetry and long range order, such as the Pinwheel Tiling, are still not well understood. In this talk we will construct C*algebras from the dynamical system associated with such a tiling. When the tiling has a substitution rule we produce a particularly tractable C*subalgebra which is classifiable. This work extends the construction of Kellendonk and Putnam.Tuesday,
9 October 2007,
Walter van Suijlekom, Radboud University
Renormalization of gauge fields using Hopf algebras
We discuss the ConnesKreimer Hopf algebra of renormalization in the case of gauge theories. We show that the SlavnovTaylor identities  which are the quantum analogues of the classical gauge symmetry  are compatible with the Hopf algebra structure, in that they generate a Hopf ideal. Consequently, the quotient Hopf algebra is welldefined and has those identities built in. This provides a rigorous proof of compatibility of the SlavnovTaylor identities with renormalization.Oct. 4 Roman Sasyk Oct. 2
Lon Mitchell (Virginia Commonwealth University)
Oct. 1
Soren Eilers (University of Copenhagen and the Fields Institute)
From substitutions to tilings and C*algebras
A (rather complicated) computation of the Kgroups of the C*algebras associated by work of Matsumoto to substitutionaldynamical systems leads to a new and computable invariant for flow equivalence of such systems. The description of this invariant, obtained in joint work with Carlsen, as a stationary inductive system involves certain socalled augmented matrices, and the fact that these lead to flow invariants is far from intuitive. However, an alternative approach by Barge and Smith gives substantial input to the understanding of this phenomenon and promises a better understanding of the equivalence relation induced by stable isomorphism of Matsumoto algebras.Sept. 27
Yasuyuki Kawahigashi (University of Tokyo)
Conformal field theory and representation theory of von Neumann algebras.Sept. 25
Stefanos Orfanos (Purdue University) Sept. 13
Ken Davidson
Operator algebras of rank 2 graphs
Sun Wei (University of Oregon)
Dynamical systems on products of Cantor set and the circleSept. 11
Nikolay Ivanov
The KTheory of Toeplitz C*Algebras of RightAngled Artin GroupsSept. 6
Benjamin ItzaOrtiz
Minimal automorphisms of C*algebrasSept. 4
Eberhard Kirchberg (HumboldtUniversität zu Berlin) Aug. 23
Adam Sierakowski
Transformation group and C*algebrasAug. 23
Leonel Robert Aug. 23
Todd Kemp (MIT)
Haagerup inequalities and semigroup contractions properties in free probabilityAug. 16 Daniel Markiewicz (Technion  Israel Institute of Technology) Aug. 14
Alin Ciuperca (University of Toronto) Aug. 9
DanVirgil Voiculescu (University of California, Berkeley)
Free analysisAug. 7
Santanu Dey (ErnstMoritzArndtUniversitat) Aug. 2
Ivan Dynov (MaxPlanckInstitute for Mathematics)
Type III factors generated by regular representations of infinitedimensional nilpotent groups.
Abstract: We discuss analogues of regular representations of two groups of uppertriangular matrices of arbitrary order as defined and studied by Alexander Kosyak. The representations are defined in terms of gaussian measures on the space of infinite uppertriangular matrices. Further we consider von Neumann algebras generated by these representations and discuss their type (in the factorial case).July 31
Trieu Le (University of Toronto)