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Conference photo for ECOAS 2022 at Michigan State University

Program

All activities held in Wells Hall. Talks held in B122 Wells Hall. Breaks and lunch held in D101 Wells Hall.

Saturday, October 22nd

08:30-09:00 am | Welcome and Coffee
09:00-09:45 am | Benjamin Hayes (University of Virginia): Property (T) and strong 1-boundedness for von Neumann algebras (Notes)

I will discuss joint work with Jekel-Kunnawalkam Elayavalli where we show that finitely generated, Property (T) algebras are strongly 1-bounded, generalizing previous work of Voiculescu, Ge-Shen, Jung-Shlyakhtenko, Jung, and Shlyakhtenko. Prior knowledge of Property (T), strong 1-boundedness, or free entropy theory will not be assumed. I will largely stick to the case of von Neumann algebras of Property (T) groups.

10:00-10:30 am | Hui Tan (University of California, San Diego): Spectral gap characterizations of property (T) for II1 factors (Slides)

I will discuss characterizations of property (T) for II1 factors by weak spectral gap in inclusions into tracial von Neumann algebras. I will explain how this is related to the non-weakly-mixing property of the bimodules containing almost central vectors, where we obtain a II1 factor version of a characterization of property (T) of Bekka and Valette.

10:40-11:00 am | Coffee Break
11:00-11:45 am | Arundhathi Krishnan (University of Waterloo): Markovianity and the Thompson Group F (Slides)

We show that representations of the Thompson group F yield a large class of bilateral stationary noncommutative Markov processes. As a partial converse, bilateral stationary Markov processes in tensor dilation form (and in particular, in the commutative setting) are shown to yield representations of F. We point out analogous results between unilateral stationary Markov processes and representations of the Thompson monoid F+. This is joint work with Claus Koestler and Stephen J. Wills.

12:00-01:30 pm | Conference Lunch catered by Woody's Oasis
01:30-02:15 pm | Michael Montgomery (Dartmouth College): Building finite dimensional representations of fusion algebras with biunitaries (Notes)

A commuting square can be characterized by an array of complex numbers called a biunitary. In this talk we will build a planar algebra associated to the commuting square and identify the biunitary as an element in this planar algebra. The biunitary can be used to embed a subfactor planar algebra into the commuting square planar algebra. We then construct finite dimensional representations of the fusion algebra of the commuting square subfactor. These representations can be used to prove that many subfactors from commuting squares are infinite depth.

02:30-03:00 pm | Quan Chen (Ohio State University): K-theoretic classification of inductive limit actions of fusion categories on AF-algebras

We introduce a K-theoretic invariant for actions of unitary fusion categories on unital C*-algebras. We show that for inductive limits of finite dimensional actions of fusion categories on unital AF-algebras, this is a complete invariant. In particular, this gives a complete invariant for inductive limit actions of finite groups on AF-algebras. This is joint work with Roberto Hernández Palomares and Corey Jones (arXiv: 2207.11854).

03:10-03:30 pm | Coffee Break
03:30-04:15 pm | Konrad Aguilar (Pomona College): The quantum Gromov-Hausdorff distance and the Gromov-Hausdorff propinquity (Notes)

Rieffel's quantum Gromov-Hausdorff distance is a complete metric on the class of order unit spaces equipped with L-seminorms (a noncommutative analogue to the Lipschitz seminorm), where distance zero provides, in part, an order unit isomorphism. Latrémolière's dual Gromov-Hausdorff propinquity is a complete metric on the class of unital C*-algebras equipped with Leibniz L-seminorms (where Leibniz adds a product rule-type property), where distance zero provides, in part, a *-isomorphism. We will show that if we define a version of the Gromov-Hausdorff propinquity for order unit spaces (and forget the Leibniz property), then we recover exactly the quantum Gromov-Hausdorff distance. As a consequence, we are able to place L-seminorms on the Bunce-Deddens algebras for which the standard circle algebras that form the Bunce-Deddens algebras converge in the quantum Gromov-Hausdorff distance by utilizing Latrémolière's completeness argument. We will also discuss more recent work where we define a version of the Gromov-Hausdorff propinquity on the class of unital C*-algebras equipped with strongly Leibniz L-seminorms (where strongly adds a quotient rule-type property) to provide new strongly Leibniz L-seminorms. (This talk includes joint work with Stephan Ramon Garcia, Elena Kim, Frédéric Latrémolière, and Timothy Rainone).

04:30-05:15 pm | Lara Ismert (Embry-Riddle Aeronautical University): Quantum graphs and their infinite path spaces (Slides)

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.

Sunday, October 23nd

08:30-09:00 am | Coffee
09:00-09:45 am | Magdalena Georgescu (University of Victoria): Cuntz-Pimsner algebras arising from C*-correspondences over commutative C*-algebras (Slides)

Consider X an infinite compact metric space, V a locally trivial vector bundle over X and α:XX a homeomorphism (often assumed minimal). We can construct a C*-correspondence E over C(X) from the module of sections of V, where we use the homeomorphism α to twist the left multiplication. As we shall see, many tractable and interesting C*-correspondences over C(X) do in fact arise in this manner.
In this talk, I will discuss some of the structural properties of the resulting Cuntz-Pimsner algebra O(E). Under the additional assumption that V is a line bundle the Cuntz-Pimsner algebra is a generalized crossed product, suggesting additional means of investigation. For Cuntz-Pimsner algebras arising from line bundles we can identify a large subalgebra of O(E). I will describe this subalgebra and list some of the consequences of this result. This is based on joint work with Adamo, Archey, Forough, Jeong, Strung and Viola.

10:00-10:30 am | Samantha Brooker (Arizona State University): Pullback diagrams of relative Toeplitz graph algebras (Slides)

Relative Toeplitz algebras of directed graphs were introduced by Spielberg in 2002 to describe certain subalgebras corresponding to subgraphs. They can also be used to describe quotients of graph algebras corresponding to subgraphs. We use the latter relationship to answer a question posed in a recent paper regarding pushout diagrams of graphs that give rise to pullback diagrams of the respective graph C*-algebras. We introduce a new category of relative graphs to this end, and we prove our results using graph groupoids and their C*-algebras. This is joint work with Jack Spielberg.

10:40-11:00 am | Coffee Break
11:00-11:45 am | Changying Ding (Vanderbilt University): Properly proximal von Neumann Algebras (Notes)

Properly proximal groups were introduced recently by Boutonnet, Ioana, and Peterson, where they generalized several rigidity results to the setting of higher-rank groups. In this talk, I will how the notion of proper proximality fits in the setting of von Neumann algebras. I will also describe several applications, including that the group von Neumann algebra of a non-amenable inner-amenable group cannot embed into a free group factor, which solves a problem of Popa. This is joint work with Srivatsav Kunnawalkam Elayavalli and Jesse Peterson.

12:00-12:30 pm | Samantha Pilgrim (University of Hawaiʻi at Mānoa): Large-Scale Dynamics and Geometric Group Theory

The dynamic asymptotic dimension (DAD) was first introduced by Guentner, Willett, and Yu to study the K-theory and nuclear dimension of crossed products (among other things). We will discuss the relationship between the asymptotic dimension of box spaces of groups and the DAD of group actions on profinite completions; as well as some dimension-theoretic properties of DAD. Together, these results allow us to calculate the dimension of box spaces of many elementary amenable groups, specifically the Baumslag-Solitar groups BS(1, n). Time allowing, we may discuss a similar relationship between DAD and warped cones.

Registration

All participants, including invited speakers, are asked to register through this form by September 25. Funding may be requested on the registration form through September 11, with priority given to graduate students, postdocs, and researchers otherwise lacking NSF support. Funding recipients will be notified by September 23.

Travel Information

Michigan State University is located in East Lansing, Michigan. If traveling by plane, it is recommended you either: (a) fly into Detroit Metro Airport (DTW) and book a seat on the Michigan Flyer shuttle service to downtown East Lansing; or (b) fly into the Capital Region International Airport (LAN) in Lansing and take a rideshare/taxi to East Lansing. If traveling by train, the East Lansing Amtrak Station is southwest of MSU campus and within walking distance to Wells Hall. If driving, there is free (overnight) parking in Ramp #5 starting 6:00 pm Friday until 6:00 am Monday. There is also free daytime parking on weekends outside of Wells Hall in Lot 39.

Accommodations

A room block has been reserved in the Graduate East Lansing (0.8 miles from Wells Hall) at a special rate of $129 per night. To make a reservation with this rate either use this link to book online or call them at (517) 348-0900 and say you are part of the MSU Operator Algebras group. Reservations should be made by September 25 to guarantee availability. Additional hotels in the area include:

Participants

  • Konrad Aguilar, Pomona College
  • Dulanji Narmada Nikethani Amaraweera Kalutotage, University of Iowa
  • ​​Juan Felipe Ariza Mejia, University of Iowa
  • Georgios Baziotis, University of Delaware
  • ​​Dipanwita Bos, University of Houston
  • Samantha Brooker, Arizona State University
  • Julio Caceres, Vanderbilt University
  • Quan Chen, Ohio State University
  • Keshav Dahiya, Indiana University–Purdue University Indianapolis
  • Patrick DeBonis, Purdue University
  • Alonso Delfin, University of Oregon
  • Rolando de Santiago, Purdue University
  • Dumindu de Silva, Vanderbilt University
  • Changying Ding, Vanderbilt University
  • Owen Ekblad, Michigan State University
  • Adriana Fernandez Quero, University of Iowa
  • Daniel Flores, Elon University
  • Felipe Flores, University of Virginia
  • Magdalena Georgescu, University of Victoria
  • Forrest Glebe, Purdue University
  • Aldo Garcia Guinto, Michigan State University
  • ​​Hector Gaxiola Williams, California State University, Long Beach
  • Colton Griffin, Purdue University
  • James Harbour, University of Virginia
  • Lawford Hatcher, Indiana University
  • Benjamin Hayes, University of Virginia
  • Vijay Higgins, Michigan State University
  • Gage Hoefer, University of Delaware
  • Tasnim Jarin Binte Iqbal, Indiana University
  • Lara Ismert, Embry-Riddle Aeronautical University
  • Nasheed Jafri, Indiana University
  • Ilya Kachkovskiy, Michigan State University
  • Pradyut Karmakar, Ohio University
  • Andreas Alexi Kavouras, Purdue University
  • Ming-Wei Kuo, Michigan State University
  • Arundhathi Krishnan, University of Waterloo
  • Srivatsav Kunnawalkam Elayavalli, Institute for Pure and Applied Mathematics
  • ​​Yoonkyeong Lee, Michigan State University
  • Junhwi Lim, Vanderbilt University
  • Zhen-Chuan Liu, Baylor University
  • Levi Lorenzo, University of Colorado Boulder
  • ​​Meaghan Mahoney, University of New Hampshire
  • Meenakshi McNamara, Purdue University
  • Michael Montgomery, Dartmouth College
  • Iason Moutzouris, Purdue University
  • ​​Micheal O Cobhthaigh, University of New Mexico
  • Zach Pence, University of Wyoming
  • Jennifer Pi, University of California, Irvine
  • Samantha Pilgrim, University of Hawai‘i at Mānoa
  • ​​Alina Rajbhandari, University of Houston
  • Rolando Ramos, Michigan State University
  • Eric Roon, University of Arizona
  • Vincent Ruzicka, University of Wyoming
  • Jeffrey Schenker, Michigan State University
  • Manpreet Singh, University of Houston
  • Benjamin Spencer, Indiana University
  • Alberto Takase, Michigan State University
  • Hui Tan, University of California, San Diego
  • Tanvi Telang, University of Houston
  • Kai Toyosawa, Vanderbilt University
  • Vincent Villalobos, University of Illinois at Urbana-Champaign
  • ​​Hao Wan, Purdue University
  • Alan Wiggin, University of Michigan-Dearborn
  • Aoran Wu, University of Virginia

Acknowledgements

The organizers gratefully acknowledge support from National Science Foundation grants DMS-2035183 and DMS-2230405 and from the Michigan State University Department of Mathematics. We also would like to thank our volunteers: Owen Ekblad, Aldo Garcia Guinto, Ming-Wei Kuo, and Yoonkyeong Lee.

Organizers

Lucas Hall

hallluc1msu.edu

Matthew Lorentz

lorentzmmsu.edu

Brent Nelson

brentmath.msu.edu