ABSTRACTS GPOTS 2019 — Texas A&M University

Plenary talks

Kelly Bickel, Bucknell University Portraits of rational inner functions This talk focuses on the structure of two-variable rational inner functions (i.e. the two variable general- izations of finite Blaschke products) with singularities on the two torus. We analyze how singular such functions can be using information pulled from their zero sets, their unimodular level sets, and some associ- ated pictures. Time permitting, we will discuss some generalizations and complications in the three-variable setting. This is joint work with Alan Sola and James Pascoe.

March Boedihardjo, University of California, Los Angeles Brown-Douglas-Fillmore theorem for lp A version of the Brown–Douglas–Fillmore theorem for lp is obtained. Joint work with Chris Phillips.

Sarah Browne, The Pennsylvania State University Quantitative E-theory and the Universal Coefficient Theorem In recent years, many people have been working on classifying C*-algebras and these results assume the Universal Coefficient Theorem (UCT), which we would like to try to extend to a bigger class of C*-algebras. I will give a summary of the Theorem and then talk about ongoing joint work with Nate Brown on Quantitative E-theory. This aims to create a new approach to tackling results like the UCT for new classes of C*-algebras. Our inspiration is work by Oyono-Oyono-Yu, who used a quantitative approach of K-theory to prove the K¨unnethTheorem for new classes of C*-algebras.

Jos´eCarri´on, Texas Christian University Classifying ∗-homomorphisms We report on a joint project with J. Gabe, C. Schafhauser, A. Tikuisis, and S. White that develops a new approach to the classification of C∗-algebras and the homomorphisms between them.

Mahya Ghandehari, University of Delaware On non-commutative weighted Fourier algebras Beurling-Fourier algebras are analogues of Beurling algebras in the non-commutative setting. These algebras for general locally compact groups were defined as the predual of certain weighted von Neumann algebras, where a weight on the dual object is defined to be a suitable unbounded operator affiliated with the group von Neumann algebra. In this talk, we present the general definition of a Beurling-Fourier algebra, and discuss how their spectra can be identified. In particular, we determine the Gelfand spectrum of Beurling- Fourier algebras for some representative examples of Lie groups, emphasizing the connection of spectra to the complexification of underlying Lie groups. This talk is based on joint work with Lee, Ludwig, Spronk,

1 and Turowska.

Elizabeth Gillaspy, University of Montana Spectral triples and wavelets for higher-rank graphs Joint work with C. Farsi, A. Julien, S. Kang, and J. Packer has revealed that the wavelets for higher-rank graphs introduced by Farsi–Gillaspy–Kang–Packer in 2016 are intimately tied to the Pearson-Bellissard spectral triples for Cantor sets. To be precise, the infinite path space of a higher-rank graph is often a Cantor set. Investigating the associated Pearson–Bellissard spectral triple reveals that the FGKP wavelets describe the eigenspaces of the Laplace-Beltrami operators of the spectral triple. We also discuss the relationship between the measure underlying the construction of the wavelets, which was first introduced by an Huef et al in 2014, and certain Dixmier traces associated to the spectral triples. This talk will strive to be a friendly introduction to the main concepts mentioned above (spectral triples, Dixmier traces, higher-rank graphs, wavelets) and to showcase the neat connections between noncommuta- tive geometry and wavelets that appear in the setting of higher-rank graphs.

Hanfeng Li, SUNY at Buffalo Entropy and combinatorial independence Topological entropy is a numerical invariant for group actions on compact spaces or C∗-algebras. Whether the entropy is positive or not makes a fundamental difference for the dynamical haviour. When a group G acts on a compact space X, a subset H of G is called an independence set for a finite family W of subsets of X if for any finite subset M of H and any map f from M to W , there is a point x of X with sx in f(s) for all s in M. I will discuss how positivity of entropy can be described in terms of density of independence sets, and give a few applications including the relation between positive entropy and Li-Yorke chaos. The talk is based on various joint works with David Kerr and Zheng Rong.

Weihua Liu, Indiana University Bloomington The atoms of the free additive convolution of two operator-valued distributions Given two freely independent random variables X and Y , the pioneering work of Bercovici and Voiculescu on regularity questions of free convolutions showed the relation between the atoms of X,Y and the atoms of X + Y . In this work, by Voiculescus operator valued subordination functions, we study the atoms of X + Y under the assumption that X and Y are free with amalgamation over a von Neumann subalgebra B of M with respect to a trace-preserving conditional expectation. Furthermore, via the linearization trick, we provide some applications to study the kernels of selfadjoint polynomials in free variables. Joint work with Serban Belinschi and Hari Bercovici.

Zhengwei Liu, Harvard University and Tsinghua University Quantum Fourier analysis We propose a program Quantum Fourier Analysis to investigate the analytic aspects of quantum symmetries and their Fourier dualities. We introduce a topological analogue of the Brascamp–Lieb inequality. We discuss some recent results and perspectives.

2 Brent Nelson, Vanderbilt University Free products of finite-dimensional von Neumann algebras and free Araki–Woods factors In the early 90s, Dykema showed any free product of finite-dimensional von Neumann algebras equipped with tracial states is isomorphic to an interpolated free group factor (possibly direct sum a finite-dimensional algebra). In joint work with Michael Hartglass, we show that this result holds in the non-tracial case when the interpolated free groups factors are replaced by Shlyakhtenko’s free Araki–Woods factors (equipped with their free quasi-free states). In particular, free products of finite-dimensional von Neumann algebras are now completely classified up to state-preserving isomorphisms. Our methods use our other recent joint work, where we show free Araki–Woods factors arise as the diffuse component of certain von Neumann algebras associated to finite, connected, directed graphs equipped with edge-weightings. In this talk I will discuss these results and show how the graph methodology is used in a simple but essential case.

Sorin Popa, UCLA The ubiquitous hyperfinite II1 factor

The hyperfinite II1 factor R has played a central role in operator algebras ever since Murray and von Neumann introduced it, some 75 years ago. It is the unique amenable II1 factor (Connes 1976), and the smallest, as it can be embedded in multiple ways in any other II1 factor M. Many problems in operator algebras could be solved by constructing “ergodic” such embeddings R,→ M. I will revisit such results and applications, and present some new results along these lines: (1) Any separable II1 factor M admits coarse embeddings of R; (2) Any separable II∞ factor admits ergodic embeddings of R.

Leonel Robert, University of Louisiana at Lafayette Extended Choquet simplices By a theorem of Lazar and Lindenstrauss, a metrizable Choquet simplex is a projective limit of finite dimensional simplices. This theorem has implications for C*-algebras: Any metrizable Choquet simplex arises as the space of tracial states of a simple separable unital AF C*-algebra. In the investigations on the structure of a C*-algebra, another space of traces is also of interest; namely, the lower semicontinuous traces with values in [0, ∞] (the extended nonnegative real numbers). These traces form a non-cancellative topological cone. The simplest example of one such cone is [0, ∞]. Problem: Characterize through axiomatic properties those cones that are expressible as projective limits of finite powers of [0, ∞]. These are also the cones of lower semicontinuous [0, ∞]-valued traces on AF C*-algebras. I will discuss the solution to this problem. This is joint work with Mark Moodie.

Christopher Schafhauser, York University On the classification of simple nuclear C∗-algebras A conjecture of George Elliott dating back to the early 1990’s asks if separable, simple, nuclear C∗-algebras are determined up to isomorphism by their K-theoretic and tracial data. Restricting to purely infinite algebras, this is the famous Kirchberg-Phillips Theorem. The stably finite setting proved to be much more subtle and has been a driving force in research in C∗-algebras over the last 30 years. A series of breakthroughs were made in 2015 through the classification results of Elliott, Gong, Lin, and Niu and the quasidiagonality theorem of Tikuisis, White, and Winter. Today, the classification conjecture is now a theorem under two additional regularity assumptions: Z-stability and the UCT. I will discuss recent joint work with Jos´eCarri´on,Jamie Gabe, Aaron Tikuisis, and Stuart White which provides a much shorter and

3 more conceptual proof of the classification theorem in the stably finite setting.

Dimitri Shlyakhtenko, UCLA Representing interpolated free group factors as group factors In a joint work with Sorin Popa, we construct a one parameter family of ICC groups G(t), with the property that the group factor of G(t) is isomorphic to the interpolated free group factor L(F (t)). Moreover, the groups G(t) have fixed cost t, are strongly treeable and freely generate any treeable ergodic equivalence relation of same cost.

Paul Skoufranis, York University Non-microstate bi-free entropy The notions of free entropy developed by Voiculescu have had a profound impact on free probability and operator algebras. In this talk, joint work with Ian Charlesworth will be discuss that generalizes the notion of non-microstate free entropy to the bi-free setting. In particular, the notions of free derivations, conjugate variables, Fisher information, and entropy are extended to handle pairs of algebras from which many interesting results, complications, and questions arise. f

Xiang Tang, Washington University in St. Louis Analytic Grothendieck–Riemann–Roch theorem In this talk, we will introduce an interesting index problem naturally associated to the Arveson–Douglas conjecture in functional analysis. This index problem is a generalization of the classical Toeplitz index theorem, and connects to many different branches of Mathematics. In particular, it can be viewed as an analytic version of the Grothendieck–Riemann–Roch theorem. This is joint work with R. Douglas, M. Jabbari, and G. Yu.

Dan-Virgil Voiculescu, UC Berkeley A hydrodynamic exercise in free probability: free Euler equations The Euler equations for a flow which preserves the Gaussian measure on Euclidean space can be translated in terms of Gaussian random variables, which raises the question of a free probability analogue. We derive free Euler equations by applying the approach of Arnold to a Lie algebra of infinitesimal automorphisms of the von Neumann algebra of a free group. We extend these equations to noncommutative vector fields satisfying weaker noncommutative smoothness conditions. We also introduce a cyclic vorticity and show that it satisfies appropriate vorticity equations and that it gives rise to a family of conserved quantities.

Parallel sessions

Tattwamasi Amrutam, University of Houston On intermediate C∗-sub-algebras of crossed products of C∗-simple group actions In this talk, we examine the structure of the intermediate C∗-algebras sitting between the reduced C∗- algebra and the reduced crossed product for C∗-simple group actions. Using the new notion of stationary C∗-dynamical systems, introduced by Yair Hartman and Mehrdad Kalantar, we show that, for a minimal action of a C∗-simple group Γ on a compact Hausdorff space X, every unital Γ − C∗-subalgebra of the

4 ∗ reduced crossed product C(X) or Γ is Γ-simple. We also show that, for a large class of actions of C -simple groups Γ y A, including non-faithful action of any hyperbolic group with trivial amenable radical, every ∗ ∗ ∗ intermediate C -algebra B, Cλ(Γ) ⊆ B ⊆ A or Γ, is of the form A1 or Γ, A1 is a unital Γ − C -subalgebra of A. A similar result holds for intermediate von Neumann algebras as well. Moreover, We shall give an example of a faithful action of a C∗-simple action on a unital C∗-algebra A for which the above result holds, namely the Odometer actions, leaving us with the question of whether there are other faithful actions for which such a result is true. Parts of this work are joint with Mehrdad Kalantar and Yongle Jiang.

Konrad Aguilar, Arizona State University Inductive limits of C*-algebras and compact quantum metric spaces We place quantum metrics, in the sense of Rieffel, on certain unital inductive limits of C*-algebras built from quantum metrics on the terms of the given inductive sequence with certain compatibility conditions. One of these conditions is that the inductive sequence forms a Cauchy sequence of quantum metric spaces in the dual Gromov–Hausdorff propinquity of Latremoliere. Since the dual propinquity is complete, this will produce a limit quantum metric space. Based on our assumptions, we then show that the C*-algebra of this limit quantum metric space is C*-isomorphic to the given inductive limit, which finally places a quantum metric on the inductive limit. This then immediately allows us to establish a metric convergence of the inductive sequence to the inductive limit. Another consequence to our construction is that we place new quantum metrics on all unital AF algebras that extend our previous work with Latremoliere on unital AF algebras equipped with faithful tracial state.

Rene Ardila, Grand Valley State University Automorphism groups of Hardy algebras Let E be a W ∗-correspondence and let H∞(E) be the associated Hardy algebra. The unit disc of inter- twiners D((Eσ)∗) plays a central role in the study of H∞(E). We show a number of results related to the automorphism groups of both H∞(E) and D((Eσ)∗). We find a matrix representation for these groups and describe several features of their algebraic structure.

Alex Bearden, The University of Texas at Tyler A module version of the weak expectation property An operator space X is said to have the weak expectation property (WEP) if the canonical inclusion X,→ X∗∗ factors through an injective operator space. We introduce a module version of the WEP for operator modules over completely contractive Banach algebras A. We prove many general results (for example, characterizing the A for which A-WEP implies WEP) and also focus particularly on the cases when A = L1(G) and A = A(G) for a locally compact group G. A highlight of our work is a locally compact analogue of Lance’s famous result for discrete groups that amenability is equivalent to WEP for the reduced C∗-algebra. This is joint work with Jason Crann and Mehrdad Kalantar.

David Blecher, University of Houston Contractive projections and maps on operator algebras We study contractive projections on algebras of operators on a Hilbert space. For example we generalize and find variants of certain classical results on contractive projections on C*-algebras and JB algebras due to Choi, Effros, Stormer, and others. In previous work we had done the ‘completely contractive case We also present many new general results about real positive maps, and give a new Banach–Stone type theorem

5 for isometries between our algebras. Applications of this are given. (Joint work with Matt Neal).

Marek Bo˙zejko, Wroclaw University and Polish Academy of Sciemces Generalized Brownian motion and positive definite functions on permutation (Coxeter) groups with appli- cations to free, Boolean and Coxeter probability and operator spaces A new class of positive definite functions related to colour-length function on permutation (Coxeter) groups is introduced. They are extensions of Riesz product on Rademacher (Abelian Coxeter) free groups to Riesz- Coxeter product on arbitrary Coxeter group (W, S). Applications to harmonic analysis (S is Sidon sets), operator spaces and free, Boolean and Coxeter probability probability will be presented. Main results are from my papers M. Bozejko, S. Gal and W. Mlotkowski, Positive Definite Functions on Coxeter groups with Applications to Operator Spaces and Noncommutative Probability, Comm. Math. Phys. 361(2), 583- 604, 2018, S. Belinschi, M. Bozejko, F. Lehner, R. Speicher, The Normal Distribution is Free infinitely divisible, Adv. Math. 226(4), 3677-3698 (2011), M. Bozejko, R. Speicher, Interpolations between bosonic and fermionic relations given by generalized Brownian motion, Math. Z. 222, 135-159, (1996), M. Bozejko, Positive definite functions on the free group and the non commutative Riesz product, Boll. Un. Math, Ital. 5A (1986), 13-22.

Chris Bruce, University of Victoria Semigroup C*-algebras associated with arithmetic progressions Congruence monoids in the ring of integers are given by certain unions of arithmetic progressions. To each congruence monoid, there is a canonical way to associate a semigroup C*-algebra. I will explain this construction and then discuss joint work with Xin Li on K-theoretic invariants. I will also indicate how all of this generalizes to congruence monoids in the ring of integers of an arbitrary algebraic number field.

Ian Charlesworth, University of California, Berkeley Free Stein information I will speak on recent joint work with Brent Nelson, where we introduce a free probabilistic regularity quantity we call the free Stein information. The free Stein information measures in a certain sense how close a system of variables is to admitting conjugate variables in the sense of Voiculescu. I will discuss some properties of the free Stein information and how it relates to other common regularity conditions.

Alexandru Chirvasitu, SUNY at Buffalo Measuring group actions on operator algebras Consider a compact quantum group G acting on an operator algebra A. The local triviality dimension of the action is a numerical invariant introduced by Gardella, Hajac, Tobolski and Wu as a non-commutative analogue of the so-called Schwarz genus of the action in the classical case, when G is a plain compact group and A consists of the continuous functions on a compact Hausdorff space X: the smallest number of open sets covering X/G and trivializing the bundle X → X/G. We give examples of dimension computations for various classes of actions (e.g. gauge actions on graph C∗-algebras) and discuss phenomena that distinguish the non-commutative version of this story from its classical counterpart. (Joint with Piotr M. Hajac, Benjamin Passer and Marius Tobolski.)

6 Chian Yeong Chuah, Baylor University A characterization for l2-radial completely positive multipliers on free groups In this talk, we will give a brief account about the relationship between radial positive-definite functions on free groups and the moments of probability measures on the interval [−1, 1]. The case for the commutative setting is proven by Bochner. Meanwhile, Haagerup and Knudby proved the case for l1 radial positive definite function. We explore the case for l2 radial positive definite functions (completely positive Fourier multipliers) on free groups.

Alan Czuron, University of Houston On the fixed point property of affine actions on Lp spaces It is known that Kazhdan’s (T) property is equivalent to the Serre’s Property (FH), also known as the property of the fixed point of affine isometric actions on a Hilbert space. The generalization of FH’s properties to other Banach spaces seems to be poorly understood. During the lecture I will sumfmarize the latest knowledge regarding this property. In particular I will present new results on the fixed point property for measure preserving affine actions on Lp spaces.

Sayan Das, The University of Iowa Group actions and subfactors In this talk I will describe a classification of all intermediate subfactors of finite index arising from a pmp action of an icc group. I will also give some applications towards the study of rigidity phenomenon arising from actions of residually finite groups. This talk is based on a recent joint work with Prof. Ionut Chifan.

Cl´ement Dell’Aiera, University of Hawai’i The restriction principle and the K¨unneth Formula We will present our joint work with Christian Bnicke on the restriction principle for ample groupoids. Simplifying a little bit, this principle, developed by Chabert, Echterhoff and Oyono-Oyono, tells us that, under suitable conditions, the K-theory of the reduced C*-algebra of a group can be computed from those of its compact subgroups. We will see how this can be adapted to groupoids and how it can be applied for establishing the K¨unneth formula for uniform Roe algebras of metric spaces.

Daniel Drimbe, University of Regina Prime II1 factors arising from actions of product groups

In this talk we show that any II1 factor associated to a free ergodic probability measure preserving action Γ y X of a product Γ = Γ1 × · · · × Γn of icc hyperbolic, free product or wreath product groups is prime, provided Γi y X is ergodic, for any 1 ≤ i ≤ n. We also present a unique prime factorization result for any II1 factor arising from a free ergodic probability measure preserving action of a product of icc, hyperbolic, property (T) groups.

Dorin Dumitrascu, Adrian College The Hodge-Dirac asymptotic morphism of an infinite-dimensional Fredholm manifold Let M be a smooth Fredholm manifold modeled on a separable infinite-dimensional Euclidean space E. We ∗ associate to M an asymptotic morphism A(M) 99K SK, where A(M) is the graded C -algebra constructed by Dumitra¸scuand Trout and SK is a direct limit of graded suspensions of compact operators. When

7 M = E we obtain the asymptotic morphism used in the inverse to the Bott periodicity map of Higson– Kasparov–Trout for the Euclidean space E. This reports on joint work with Jody Trout.

Anna Duwenig, University of Victoria Non-commutative Poincar´eduality of the irrational rotation algebra The irrational rotation algebra is known to be Poincar self-dual in a KK-theoretic sense. The required K-homology fundamental class has been constructed by Connes out of the Dolbeault operator on the 2- torus, but so far, there has not been an explicit description of the dual element. In this talk, I will geometrically construct a finitely generated projective module representing said K-theory class, by using a pair of transverse Kronecker flows on the 2-torus. This is joint work with Heath Emerson.

Kari Eifler, Texas A&M University Non-local games and the graph isomorphism game Non-local games give us a way of observing quantum behaviour through the observation of only classical data, and there are several different mathematical models to consider. The graph isomorphism game is important in quantum information theory and is an example of a non-local game. We show that the *- algebraic, C∗-algebraic, and quantum commuting (qc) notions of a quantum isomorphism between classical graphs X and Y are all equivalent.

Keenan Eikenberry, Arizona State University Stacks of C*-categories A stack is essentially a category-valued sheaf. Algebraic stacks are ubiquitous in algebraic geometry, and their topological and smooth counterparts have received increasing attention as of late. In this talk, I will show that stack structures also occur naturally in operator algebraic settings. Such structures should be broadly useful. In particular, though, I will show that our construction can be used to put a topology on the set of (isomorphism classes of) objects in a C*-category. In this manner, we obtain a sort of categorified topological vector space. Further, using a technique from O’Sullivan, we can also topologize the collection of morphisms in a C*-category, thereby obtaining C*-categories internal to the category of topological spaces. (Joint work with Corey Jones.)

Li Gao, Texas A&M Univeristy Quantum majorization via operator space duality Quantum majorization defines the relation that a bipartite quantum state can be converted to another bipartite state via quantum operation local at one system. In a recent paper, Gour et al give a complete characterization of quantum majorization using entropy inequalities. In this talk, I will discuss these entropy inequalities via operator space tensor product and duality. This enable us to extend Gour et al’s result to infinite dimensional system as well as hyperfinite von Neumann algebras. Connections to matrix convex sets and vector-valued noncommutative Lp space will also be mentioned. This is a joint work with Priyanga Ganesan, Satish Pandey and Sarah Plosker.

Samuel Harris, University of Waterloo Crossed products of operator systems We consider different crossed product constructions for a discrete group action on an operator system via

8 complete order isomorphisms. In analogy to the work of E. Katsoulis and C. Ramsey, we describe two canonical crossed products arising from such an operator system dynamical system: the full enveloping crossed product and the full crossed product. We will discuss some of the properties of these crossed products, and how (relative full) operator algebra crossed products can be encoded in (relative full) operator system crossed products. Finally, using A. Kavruk’s notion of operator systems that detect nuclearity, we give a negative answer to a question on full relative operator algebra crossed products posed by E. Katsoulis and C. Ramsey.

Ben Hayes, University of Virginia Maximally rigid subalgebras of reversible deformations I will discuss ongoing joint work with Rolando de Santiago, Daniel Hoff, and Thomas Sinclair. In it, we investigate reversible deformations in the sense of Popa. We show that (under some mixing conditions) any diffuse subalgebra on which the deformation is rigid is uniquely contained in a maximal rigid subalgebra. We establish permanence properties of these subalgebras, discuss some applications, along with applications to L2-rigidity. Connections to L2-cohomology and L2-Betti numbers of groups will be discussed as well.

Paul Herstedt, University of Oregon Purely infinite C*-algebras with the ideal property In the non-simple case, there are many notions of pure infiniteness (some are known to not agree, but many questions are still open). With nice regularity conditions on a purely infinite C*-algebra, such as approximately divisibility or the ideal property, some of these notions are known to agree. We expand on work done by Pasnicu and Rørdam (in 2006), by using scaling elements to give new conditions for when a C*-algebra is purely infinite and has the ideal property.

Cristian Ivanescu, MacEwan University Pedersen ideals of tensor products of non-unital C*-algebras and applications Properties of the algebra of compactly supported continuous functions are captured in the noncommutative setting by the Pedersen ideal. We show that positive elements of the Pedersen ideal of a tensor product can be approximated in a strong sense by sums of tensor products of positive elements. This has a range of applications to the structure of tracial cones and related topics that will be described. This is a joint work with Dan Kucerovsky.

David Jekel, University of California, Los Angeles Free entropy and transport for free Gibbs states from convex potentials We present a new approach to the theory of convex free Gibbs states and their associated random matrix models, that makes the connections between classical and free probability more explicit, and relies on PDE rather than SDE techniques. Consider a probability measure µN on m-tuples of self-adjoint N ×N matrices 2 −N VN m with density (1/ZN )e , where VN : MN (C)sa is uniformly convex and semi-concave. Assuming that sequence of the normalized gradients DVN has “asymptotically approximable by trace polynomials,” we show that the measures µN “converge” to some non-commutative law λ. Moreover, the classical entropy and Fisher information of µN converges to the free entropy and Fisher information of λ. Finally, we construct transport from µN to the law of a GUE tuple and from λ to the law of a semicircular tuple.

9 Georgios Katsimpas, York University R-diagonal operators in bi-free probability In the theory of free probability, an operator a is called R-diagonal if the R-transform (i.e. the free analogue for the logarithm of the Fourier transform) of the pair (a, a∗) is of a specific form, which is in a certain sense diagonal. The R-diagonal operators constitute a class of particularly well-behaved non-normal operators and their distributions yield answers to maximization problems involving free entropy. Bi-free probability theory was originated by Voiculescu as an extension of the free setting and involves the simultaneous study of left and right action of algebras on reduced free product spaces. By making use of the combinatorial description of bi-free probability, developed by Charlesworth, Nelson and Skoufranis, we will present the bi-free analogue of R-diagonal operators, namely bi-R-diagonal pairs of operators, and discuss a number of their salient features in the bi-free framework.

Se Jin Kim, University of Waterloo Hyperrigidity for C*-correspondences The Hao-Ng isomorphism problem asks: if G is a locally compact group acting on a non-degenerate C*- correspondence (C,X), when is it the case that we have the identity

OC (X) o G = OCoG(X o G)? Hao and Ng verify this identity for any amenable locally compact group G. In recent work, Katsoulis and Ramsey are able to show that whenever (C,X) attains a property called hyperrigidity, the crossed product OC (X) o G is always a Cuntz-Pimsner algebra associated to a C*-correspondence arising from a certain completion of (Cc(G, C),Cc(G, X)). In this talk we describe an exact characterization of hyperrigidity for C*-correspondences. This generalizes the work of Dor-On and Salomon which gives a characterization for C*-correspondences associated to discrete graphs and the work of Katoulis and Ramsey, which give a sufficient condition in the case when X is countably generated over C.

Slawomir Klimek, IUPUI Odometers and derivations I will describe decompositions and structure of unbounded derivations in a crossed product algebra of an odometer. I will also discuss derivations in a Toeplitz extension of the crossed product and the question whether unbounded derivations can be lifted from one algebra to the other.

Amudhan Krishnaswamy-Usha, Texas A&M University Angles between Haagerup-Schultz projections for operators in a finite von Neumann algebra For operators in a finite tracial von Neumann algebra, there is a nice associated measure called the Brown measure (for normal operators, this is just the spectral measure). Haagerup and Schultz proved that these operators also have a family of invariant projections, which behave well with respect to the Brown measure. We show that if the angles between these projections are bounded away from zero, there exists a decomposition which can be thought of as the analogue of the Jordan normal form for matrices. This is related to the notion of spectral and scalar-type operators, introduced by Dunford in the ’50s. We use this to show that Voiculescu’s circular operator is not spectral. This includes joint work with Ken Dykema.

10 Mahtab Lak, University of New Hampshire General reflexivity for absolutely convex sets In 1994 D. Hadwin introduced the notion of a reflexivity triple (X,Y,E) and defined a very general notion of reflexivity, called E-reflexivity, for a linear subspace of the vector space X. Hadwin’s general version included many special versions (algebraic reflexivity, topological reflexivity, approximate reflexivity, hyperreflexivity) that had been studied for linear spaces of linear transformations on a vector space or Hilbert space. In this thesis we extend Hadwin’s notion and define and study the abstract notion of reflexivity for an absolutely convex subset of X. We have extended many of Hadwin’s results and obtained some new ones. We have also extended Hadwin’s generalized notion of direct integrals from measurable families of linear spaces to absolutely convex sets.

Nicholas LaRacuente, University of Illinois at Urbana-Champaign Complete logarithmic Sobolev inequality for quantum Markov semigroups from irreducible graphs We derive a complete logarithmic Sobolev inequality (CLSI) for quantum Markov semigroups (QMSs) with particular forms. Here the ”complete” aspect means that our estimates hold even under tensoring with an arbitrarily large auxiliary system, which also implies tensor-stability. The CLSI allow us to estimate the rate at which a density in a QMS decays towards an invariant subalgebra. We use a transference technique to connect decay times to the return times of Markov processes with transitions described by finite, symmetrically weighted, ergodic graphs. Our estimates depend on the spectral gap of the graph Laplacian and the number of vertices in the graph, but not explicitly on the dimension of the state space. QMSs describe a physical process known as decoherence, an ubiquitous and primary challenge in quantum computing. This is joint work with Li Gao and Marius Junge.

Hung-Chang Liao, University of Ottawa Diagonal dimension of C*-pairs Nuclear dimension of C*-algebras, a noncommutative version of topological covering dimension, has been playing a central role in classifying simple separable nuclear C*-algebras. For C*-algebras built from dynam- ical objects, one can often show that a (finite-)dimension type property of the underlying object implies that the associated C*-algebra has finite nuclear dimension, although in general one cannot expect the converse to be true. Diagonal dimension refines the nuclear dimension in that its completely positive decompositions keep track of a prescribed abelian subalgebra, and hence retains more information of the underlying objects. For example, the asymptotic dimension of a countable discrete group is captured by the diagonal dimension of its uniform Roe algebras (with respect to the canonical abelian subalgebra). A similar phenomenon is found in many topological dynamical systems and topological groupoids. This is joint work with Kang Li and Wilhelm Winter.

Christopher Linden, University of Illinois, Urbana Champaign Slow continued fractions, Cuntz algebras, and Road coloring By work of Glimm, the representation theory of the Cuntz algebras is intractable. This difficulty can be avoided either by specializing to a subclass of representations, or by weakening the notion of equivalence. In this talk we discuss recent work from both approaches, applying tools from number theory and graph theory, respectively. The latter is joint work with Adam Dor-On.

11 Wenjing Liu, University of New Hampshire A characterization of tracially nuclear C*-algebras We give two characterizations of tracially nuclear C*-algebras. The first is that the finite summand of the second dual is hyperfinite. The second is in terms of a variant of the weak* uniqueness property. The necessary condition holds for all tracially nuclear C*-algebras. When the algebra is separable, we prove the sufficiency.

Zhen-Chuan Liu, Baylor University Paley’s inequality on ordered groups Paley’s inequality implies that the Fourier coefficient of the function in the Hardy space H1(T) is square summable on any lacunary set. We will introduce a similar result for the ordered nonabelian group, e.g., free group.

Terry Loring, University of New Mexico Computable formulas for the connecting maps in real or graded K-theory When working with real or Z/2 graded C*-algebras, the associated exact sequences in K-theory can be defined using E-theory or KK-theory. To make calculations more accessible, it is useful to have simple descriptions of all the K-theory groups and also the connecting maps. There are a uniqueness results on the connecting maps, generalizing a result of Elliott in the complex, ungraded case. This greatly facilitates the search for simple formulas. The motivation for finding these formulas is the desire to extend an index theorem for topological insulators to more symmetry classes. This talk covers joint work with Boersema and on-going joint work with Schulz-Baldes.

Xin Ma, Texas A&M University Comparison and regularity properties of reduced crossed products In this talk I would like to talk about comparison phenomenon in dynamical systems as a natural analogue of strict comparison in the C*-setting. In particular, I will talk about how comparison helps establish regularity properties in crossed products and how it relates to almost unperforation in type semigroups in the context of Cantor dynamical systems.

Nicholas Manor, University of Waterloo Exactness vs. C∗-exactness for certain non-discrete groups It is known that exactness for a discrete group G is equivalent to C∗-exactness, i.e., the exactness of the ∗ ∗ reduced C -algebra Cr(G). It is a major open problem to determine whether this equivalence holds for all locally compact groups, but the problem has recently been reduced by Cave and Zacharias to the case of totally disconnected (td) unimodular groups. We will discuss ways to extend the equivalence of exactness and C∗-exactness to classes of non-discrete groups. These include the td groups admitting an invariant neighbourhood of the identity, and a family of td unimodular groups introduced by Yuhei Suzuki in the context of C∗-simplicity.

Mircea Martin, Baker University Holomorphic spectral theory. A geometric approach We will introduce and analyzes several geometric, analytic, and operator theoretic concepts that pertain to

12 Holomorphic Spectral Theory in a Hilbert Space Setting, which informally consists of the part of spectral theory that relies on the use of vector and operator valued holomorphic functions. The three objects of interest that justify the development of holomorphic spectral theory — in either a single or in several complex variables — are some special classes of Hilbert space operators that generalize the Cowen–Douglas class, holomorphic mappings with values in a complex Grassmann manifold, and Hermitean holomorphic vector bundles. Among the main issues of the approach to the specific questions addressed in our talk, one should single out the Cauchy–Riemann Equations that characterize holomorphic families of closed subspaces of a complex Hilbert space, an operator theoretic form of the Gram–Schmidt Process, and a substitute in arbitrary dimension for the Generalized Grothendieck’s Lemma. The primary goal is to identify complete sets of invariants for each the three objects relative to some natural equivalence relations.

Martin Mathieu, Queen’s University Belfast Strictly singular multiplication operators on L(X)

In joint work with Pedro Tradacete (Madrid) we obtain several `p-factorization results for strictly singular operators and apply them to investigate the strict singularity of the two-sided multiplication operator on L(X) for various Banach spaces X.

Kathryn McCormick, University of Minnesota cb-Morita equivalence of some nonselfadjoint operator algebras In (Blecher, Muhly, Paulsen, 2000), the authors define two notions of Morita equivalence for (possibly nonselfadjoint) operator algebras, which they call strong Morita equivalence and cb-Morita equivalence. The latter equivalence is strictly weaker. In some situations, a cb-Morita equivalence can be factored into a strong Morita equivalence composed with a similarity; this is true for an equivalence containing a separable C∗-algebra, for instance. We will describe a few cases in which we can use a cb-Morita equivalence of C∗-algebras to more precisely pin down a cb-Morita equivalence of their subalgebras.

Gabriel Nagy, Kansas State University Simplicity criteria for ´etalegroupoid C*-algebras The main problem covered in this talk concerns simplicity of the reduced C*-algebras of ´etalegroupoids. Our proposed method focuses on the analysis of the interior isotropy bundle. Along the way we also provide non-simplicity criteria, as well as a short proof of a result of Brown–Clark–Farthing–Sims on the simplicity of the full C*-algebra. As an application, we obtain a slight sharpening of a result of Ozawa on simplicity of a reduced crossed product by a discrete group. (Joint work with Danny Crytser; to appear in JOT.)

Igor Nikolaev, St. John’s University Subfactors and Hecke groups We study a relation between the Hecke groups and the index of subfactors in a von Neumann algebra. Such a problem was raised in 1991 by V.F.R. Jones. We solve the problem using the notion of a cluster C*-algebra. This is a joint work with Andrey Glubokov. Reference: arXiv:1902.02572

Shintaro Nishikawa, Penn State University The gamma element and the (gamma) element For a second countable, locally compact, Hausdorff group G, the BaumConnes assembly map for G is

13 a mysterious homomorphism from the K-homology of co-compact, proper G-spaces to the K-theory of the reduced group C*-algebras of G. The BaumConnes conjecture states that the assembly map is an isomorphism of abelian groups for any G. The gamma element method (or the dual-Dirac method) is a versatile method to attack the conjecture. The method is initially developed by Gennadi Kasparov in 1988 and is successfully used by him and others to (partially) verify the conjecture for a large class of groups G. The main point of this method is to find the so-called gamma element for G. I will first explain and describe the gamma element and the gamma element method. Then, I will describe the newly-defined notion, the (gamma) element for G which can be used as a replacement for the gamma element.

Cornel Pasnicu, The University of Texas at San Antonio On and around the weak ideal property A C*-algebra has the weak ideal property if any nonzero quotient of ideals of the stabilization of the algebra contains a nonzero projection. This concept, a weakening of the ideal property, which has very good permanence properties, was recently introduced in a joint work with N.C. Phillips (JFA 2015). I will present some results involving the weak ideal property, its connections with some related properties (joint work with N.C. Phillips) and some recent work (in progress) related to an open problem.

Ben Passer, University of Waterloo Invariants in noncommutative Borsuk-Ulam theory If A is a unital C∗-algebra which admits a free coaction of a compact quantum group H, then the equivariant join of A and H is a unital C∗-algebra which glues a copy of A to a copy of H in a coaction-compatible way. This construction of Baum-Dabrowski-Hajac is analogous to the topological join of a compact space and a compact group, which in particular allows one to construct a sphere Sn+1 from the equator Sn and the poles. In this case, the poles are encoded as the group Z/2Z, which acts on Sn via x 7→ −x. One goal of their construction is to generalize the Borsuk-Ulam theorem: must there exist no equivariant morphisms from A to the join of A and H? We examine the role of invariants used to solve special cases of this conjecture, ultimately showing that if A and H are fundamentally noncommutative, then there can be no well-behaved integer invariant which solves the conjecture in full generality. Finally, we examine the simplest possible example which exhibits this behavior. Joint work with Alexandru Chirvasitu.

Carl Pearcy, Texas A&M University Hyperinvariant subspaces for some 2 × 2 operator matrices The speaker will discuss the problem of establishing that operators in a certain class of 2 × 2 matrices with operator entries have nontrivial hyperinvariant subspaces, including a discussion of why this problem is interesting and important, and progress made on it by the speaker and coauthors.

David R. Pitts, University of Nebraska–Lincoln Weak Cartan inclusions An inclusion is a pair of C∗-algebras (C, D), with D an abelian subalgebra of C which contains an approximate unit for C; the inclusion is regular when the set N(C, D) := {v ∈ C : v∗Dv ∪ vDv∗ ⊆ D} has dense linear span. Given a twist (Σ,G) over an ´etale,topologically free and Hausdorff groupoid G, Renault gave a simple ∗ (0) list of axioms which characterized inclusions of the form (Cred(Σ,G),C0(G )); he called such inclusions Cartan inclusions. In this talk, I will describe recent joint work with Ruy Exel in which we give a variant of

14 Renault’s result where the requirement that G be Hausdorff is dropped. Let G be an ´etaleand topologically free, but not necessarily Hausdorff, groupoid and let (Σ,G) be a twist over G. The essential groupoid ∗ ∗ ∗ C -algebra, Cess(Σ,G), is the completion of Cc(Σ,G) with respect to a C -seminorm minimial among all ∗ (0) C -seminorms on Cc(Σ,G) which agree with the norm on C0(G ). We identify the key properties of ∗ (0) inclusions of the form (Cess(Σ,G),C0(G )) to define weak Cartan inclusions. For a weak Cartan inclusion (C, D) the subalgebra D need not be maximal abelian, and there need not be a conditional expectation of C onto D. The main result is that if (C, D) is a weak Cartan inclusion (with C separable), there is a twist (Σ,G) over the ´etaletopologically free groupoid G such that (C, D) is isomorphic to the weak Cartan ∗ (0) inclusion (Cess(Σ,G),C0(G )).

Gelu Popescu, The University of Texas at San Antonio Invariant subspaces and operator model theory on noncommutative varieties We present recent results regarding the characterization of the joint invariant subspaces under the universal n model (B1,...,Bn) associated with a noncommutative variety V in a regular domain in B(H) . The main result is a Beurling–Lax–Halmos type representation which is used to parameterize the coresponding wandering subspaces of the joint invariant subspaces. We also present a characterization of the elements in the noncommutative variety V which admit characteristic functions. This leads to an operator model theory for completely non-coisometric elements which allows us to show that the characteristic function is a complete unitary invariant for this class of elements. Our results apply, in particular, in the commutative case.

John Quigg, Arizona State University Tensor D coaction functors In this report of work in progress (joint with S. Kalizewski and Magnus Landstad), I’ll describe our efforts to handle a certain exotic crossed product of Baum, Guentner, and Willett using coaction functors. In efforts to “fix” the Baum–Connes conjecture, exotic crossed products are being used to replace the reduced crossed product, and one such effort involves tensoring with a fixed action. Our work on this involves tensoring instead with a fixed coaction. When the group is discrete, we get an exact coaction functor that reproduces the [BGW] crossed product when we compose with the full-crossed-product functor. For arbitrary locally compact groups, we are making progress, but a couple of problems remain. I’ll describe both the good and the bad news.

Travis Russell, US Military Academy The geometry of the synchronous quantum correlation sets In this talk we discuss the problem of determining the geometry of the set of synchronous quantum cor- relations as a subset of Euclidean space. We provide explicit examples of how to carry this out in the three-experiment two-outcome scenario, and discuss some properties of this correlation set which arise from the computation. We also discuss some connections between these computations and Connes’ embedding conjecture.

Guy Salomon, University of Waterloo Proximal actions An action of a discrete group G on a compact Hausdorff space X is said to be proximal if for every two points x, y ∈ X there is a net gα ∈ G such that lim gαx = lim gαy, and strongly proximal if the natural action of G

15 on the space P (X) of probability measures on X is proximal. G is said to be strongly amenable if all of its proximal actions have a fixed point and amenable if all of its strongly proximal actions have a fixed point. In this talk, I will present relations between some fundamental operator theoretic concepts to proximal and strongly proximal actions, and hence to strongly amenable and amenable groups. In particular, I will focus on the C∗-algebra of continues functions over the universal minimal proximal G-action and characterize it in the category of G-operator-systems. The talk is based on joint work with Matthew Kennedy and Sven Raum.

Pieter Spaas, UC San Diego Exotic central sequence algebras We will define and discuss the central sequence algebra of a von Neumann algebra. Furthermore, we will provide examples of von Neumann algebras whose central sequence algebra is not the “tail” algebra associated to any decreasing sequence of von Neumann subalgebras, which settles a question of McDuff from the 60s. This is based on joint work with Adrian Ioana.

Jack Spielberg, Arizona State University C*-algebras of certain one-relator monoids We describe recent work on the C*-algebras associated to some monoids related to braid groups. This is joint work with Xin Li and Tron Omland.

Adi Tcaciuc, MacEwan University The Invariant Subspace Problem for rank-one perturbations The Invariant Subspace Problem is one of the most famous problem in Operator Theory, and is concerned with the search of non-trivial, closed, invariant subspaces for bounded operators acting on a separable Banach space. Considerable success has been achieved over the years both for the existence of such subspaces for many classes of operators, as well as for non-existence of invariant subspaces for particular examples of operators. However, for the most important case of a separable Hilbert space, the problem is still open. A natural, related question deals with the existence of invariant subspaces for perturbations of bounded operators. These type of problems have been studied for a long time, mostly in the Hilbert space setting. In this talk I will present a new approach to these perturbation questions, in the more general setting of a separable Banach space. I will focus on the recent history, presenting several new results that were obtained along the way with this new approach, and examining their connection and relevance to the Invariant Subspace Problem.

Mariusz Tobolski, IMPAN Rokhlin dimension for actions of non-Lie groups We discuss the connection between actions with the finite Rokhlin dimension and compact principal bundles, where Lie groups play an essential role. Then we introduce an equivalent characterization of the Rokhlin dimension of actions of compact metrizable (not necessarily Lie) groups which leads to an unexpected result: if the Rokhlin dimension of action of the group of p-adic integers on a compact metrizable space is finite then it is at most 3. Based on joint work with Eusebio Gardella, Piotr M. Hajac and Jianchao Wu.

16 Andrea Vaccaro, University of Pisa and York University Trivial embeddings of the Calkin algebra Let Q(H) be the Calkin algebra on a separable, infinite-dimensional Hilbert space. A unital embedding φ of Q(H) into itself is trivial if there is a unitary u in Q(H) and a strongly continuous, unital, *-homomorphism Φ from B(H) to B(H) lifting Ad(u)φ. We show that under the proper forcing axiom (a far reaching extension of the Baire category theorem known to be independent from ZFC) all unital embeddings of the Calkin algebra into itself are trivial. We also discuss how this implies that, under the proper forcing axiom, the class of the C*-algebras that embed into Q(H) is not closed under inductive limit and (any) tensor product.

Fredy Vides, Universidad Nacional Aut´onomade Honduras On topologically controlled matrix approximation Several interesting problems in numerical analysis in abstract spaces, can be reduced to the computation of ∗ 1 constrained representations of the universal C -algebra C(S ) in Mn(C), factoring through the commutative algebra Circ(k) of circulant matrices in Mk(C), for some integers k ≤ n. In this talk, we present some theorems that provide a relation between the aforementioned representations, and the computation of approximate numerical solutions of some related structured matrix equations, for this purpose we use elementary tools from operator K-Theory, to compute matrix analogies of the topological surgical cuts (punctures), that are applied along the lines of the topological technique known as Kirby’s torus trick. We study the solvability of the previously described matrix representation problems. Some connections of the aforementioned results, with Kirby’s work in geometric topology, are outlined.

Ami Viselter, University of Haifa Generating functionals on quantum groups We will discuss generating functionals on locally compact quantum groups. One type of examples comes from probability: the family of distributions of a L´evyprocess form a convolution semigroup, which in turn admits a natural generating functional. Another type of examples comes from (locally compact) group the- ory, involving semigroups of positive-definite functions and conditionally negative-definite functions, which provide important information about the group’s geometry. We will explain how these notions are related and how all this extends to the quantum world; see how generating functionals may be (re)constructed and study their domains; and indicate how our results can be used to study cocycles. Based on joint work with Adam Skalski.

Gary Weiss, University of Cincinnati Universal block tridiagonalization in B(H) and beyond We prove every B(H) operator on a separable infinite dimensional complex Hilbert space has a basis for which its matrix is finite block tridiagonal with the same fixed precise block sizes given in a simple exponential form. An extension to unbounded operators occurs when a certain domain of definition condition is satisfied.

Konrad Wrobel, Texas A&M University Cost of inner amenable equivalence relations Cost is a [1, ∞)-valued measure-isomorphism invariant of aperiodic equivalence relations defined by Gilbert

17 Levitt and heavily studied by Damien Gaboriau. For a large class of equivalence relations, including hy- perfinite, the cost is 1. Yoshikata Kida and Robin Tucker-Drob recently defined the notion of an inner amenable equivalence relation as an analog of inner amenability in the setting of groups. We show inner amenable equivalence relations also have cost 1. This is joint work with Robin Tucker-Drob.

Yi Yan, University of Kansas On the essential spectra of Hankel operators and commutators of Toeplitz and Hankel operators This talk aims to highlight the interaction between Toeplitz–Hankel operators on the Hardy space and function algebras of the circle. Using the Allan–Douglas localization principle in the Calkin algebra and cer- tain quasicontinuous functions, it is proved that the essential spectra of Hankel operators and commutators of Toeplitz and Hankel operators are antipodal symmetric under a mild condition on the Hankel symbol functions. Conjugates of interpolating Blaschke products and characteristic functions are constructed that satisfy the condition, while examples in certain symbol classes show the condition is only sufficient.

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