Howard Rowlee Lecture 2023

Speakers

• Chad Berner of Iowa State University
  Title: Fourier series for singular measures on the Real line
  Abstract: Any square integrable function on the torus is a norm limit of its Fourier series, but what if you change the measure from Lebesgue measure to a singular measure? It turns out you will lose orthogonality of the exponentials, but by the Kaczmarz algorithm, any function that is square integrable in this new measure space has a Fourier series converging in norm. Using an operator version of the Kaczmarz algorithm along with analytic operator theory of De Branges, we discuss further results in higher dimensions as well as if and when these results extend to the real line.
  
• Jorge Castillejos of the Institute of Mathematics UNAM
  Title: On topologically zero-dimensional morphisms
  Abstract: Non-commutative topological dimension has been a recurrent topic within C*-algebras theory. The nuclear dimension is a notion, introduced by Winter and Zacharias, which corresponds to a non-commutative form of Lebesgue covering dimension which played a key role in the classification programme of simple unital C*-algebras. A natural step forward is the classification of maps. Just as with C*-algebras, such classification requires strong regularity conditions such as nuclear dimension but now at the level of the map. In this talk, I will present a description of maps with nuclear dimension equal to zero.
  
• Michael Davis of the University of Iowa
  Title: Rigidity for von Neumann Algebras of Graph Product Groups
  Abstract: I will discuss my ongoing joint work with Ionut Chifan and Daniel Drimbe on various rigidity aspects of von Neumann algebras arising from graph product groups whose underlying graph is a certain cycle of cliques and whose vertex groups are wreath-like product property (T) groups. In particular, I will describe all symmetries of these von Neumann algebras by establishing formulas in the spirit of Genevois and Martin’s results on automorphisms of graph product groups. In doing so, I will highlight the methods used from Popa’s deformation/rigidity theory as well as new techniques pertaining to graph product algebras.
  
• Caleb Eckhardt of Miami University
  Title: Hilbert-Schmidt stability of amenable groups
  Abstract: Roughly speaking a group is Hilbert-Schmidt (HS) stable if every finite dimensional approximate unitary representation of G can be perturbed to an actual representation of G. Here ``approximate" and ``perturbed" relate to the normalized Hilbert-Schmidt norm. Recently HS-stability has attracted interest partially due to the connections to the Connes embedding problem for groups. For amenable groups Hadwin and Shulman reformulated Hilbert-Schmidt stability in terms of tracial approximations. This reformulation makes available the tools of operator algebras to be applied to HS-stability problems for amenable groups. I will give a gentle introduction to this topic and discuss recent joint work with T. Shulman showing nilpotent groups are HS-stable, showing the first examples of amenable HS-stable non-permutation stable groups and whatever else time allows.
• Menevse Eryuzlu of the University of Colorado, Boulder
  Title: Simplicity of Cuntz-Pimsner Algebras
  Abstract: In 2001 Schweizer introduced the "aperiodicity" property and proved that if _AX_A is a full C*-correspondence with injective left action and A is a unital C*-algebra, then the Cuntz-Pimnser algebra O_X is simple if and only if _AX_A is aperiodic and A has no proper invariant ideals. This result leads to a natural question: is aperiodicity an analogue of Condition (L) for graphs? In a joint work with Mark Tomforde we discovered that the answer is negative. In this talk I will present a condition, called condition (S), which is an analogue of Condition (L) for graphs. I will show that Condition (S) can be used to prove a Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner algebras, and to obtain sufficient conditions for simplicity of Cuntz-Pimsner algebras.
  
• Adam Fuller of Ohio University
  Title: Intermediate algebras in groupoid algebras
  Abstract: Let A be a C*-algebra, and let D in A be a Cartan subalgebra. It is well known (thanks to the work of Renault and Kumjian) that A having a Cartan subalgebra D means that A is isomorphic to the reduced C*-algebra of a twist over a groupoid G. In this talk we will discuss to what extent this groupoid structure determines the intermediate C^*-algebras B contained in A that contain D. In particular, we will give sufficient conditions for there to be a Galois correspondence between open subgroupoids of G containing G^{(0)} and such intermediate subalgebra B. We will further look at examples where this correspondence fails. The analogous question for Steinberg algebras will also be considered.
  This talk is based on published work with Jonathan Brown, Ruy Exel, David Pitts, and Sarah Reznikoff; and on ongoing work with Jonathan Brown and Lisa Clark.
  
• Mitch Hamidi of Embry-Riddle Aeronautical University
  Title: Distinguishing between quantum Cuntz-Krieger and local quantum Cuntz-Krieger algebras
  Abstract: Quantum graphs are noncommutative generalizations of finite graphs that have been of significant interest in recent years. In this talk, we will discuss two C*-algebras associated to a quantum graph, the quantum Cuntz—Krieger (QCK) algebra and the local QCK algebra of a quantum graph, and give the first example of a quantum graph with distinct QCK and local QCK algebras. This is based on joint work with Lara Ismert and Brent Nelson.
  
• Sam Harris of Northern Arizona University
  Title: Quantum Isomorphisms of Quantum and Classical Graphs
  Abstract: Quantized versions of graphs and their isomorphisms have been studied extensively over the past 15 years. There are many potential uses for these ideas: (quantum) graphs represent how (quantum) information can be confused when sent over a (quantum) channel. The quantum versions of graph isomorphism also arise from two-player non-local games, which provide a way to understand entanglement in quantum information theory and are deeply connected to the recently resolved Connes' embedding problem, and open problems such as the existence/non-existence of non-hyperlinear groups.
  In this talk, we will describe an approach to quantum isomorphisms of quantum graphs, using the avenue of correlations and quantum channels. This approach involves the language of concurrent quantum-input, quantum output non-local games. As time allows, we will explore the implications of this approach for classical graphs.
  Based on joint work with Michael Brannan, Ivan Todorov and Lyudmila Turowska
  
• David Pitts of University of Nebraska-Lincoln
  Title:Normalizers and Approximate Units for Inclusions of C*-Algebras
  Abstract:Consider pairs of C*-algebras (C,D) with D an abelian subalgebra of C. An element v of C normalizes D if both v*Dv and vDv* are contained in D. The pair (C,D) is regular when the linear span of the normalizers is dense in C and is singular when every normalizer belongs to D.
  I will begin with some examples, then prove a commutation result for Hermitian normalizers and discuss some consequences of this result related to familiar constructions. Sample consequence: when D is a regular MASA in C, every approximate unit for D is an approximate unit for C.
  The inclusion (C,D) is intermediate to the regular MASA inclusion (B,D) if C is contained in B. I will discuss the problem of when a pair (C,D) is intermediate to a regular MASA inclusion: this occurs for some singular MASA inclusions (C,D) but not others; however, no MASA in B(H) has this property.
  
• Lara Ismert of Embry-Riddle Aeronautical University
  Title: Quantum graphs and their infinite path spaces
  Abstract: A quantum graph is a triple that consists of a finite-dimensional C*-algebra, a state, and a quantum adjacency matrix. Analogous to the Cuntz-Krieger algebra of a classical graph, the quantum Cuntz-Krieger (QCK) algebra of a quantum graph is generated by the operator coefficients of matrix partial isometries. In this talk, we discuss connections between a QCK algebra and a Cuntz-Pimsner algebra associated to a quantum graph correspondence, and in the complete quantum graph case, connections between the QCK algebra and a particular Exel crossed product. We end by discussing the challenges in defining the "infinite path space" for a quantum graph.
  
• Stuart White of The University of Oxford
  Title: Tracially Complete C*-algebras
  Abstract: Over the last decade a major theme has been the application of von Neumann methods in the structure and classification of stably finite C*-algebras, often with the idea of explicitly lifting results back from the von Neumann level to the C*-algebra setting. This works most crisply for C*-algebras with a unique trace, where one works with the associated GNS representation. In this talk, I'll introduce the framework of tracially complete C*-algebras as a general bridge between the W* and C*-theory, and discuss structure and classification results for these new type of operator algebras.
  This is joint work with Carrion, Castillejos, Evington, Gabe, Schafhauser and Tikuisis.