The twentieth iteration of East Coast Operator Algebras Symposium (ECOAS) will be held at Purdue University October 21-22, 2023. The conference focuses on operator algebras (C* and von Neumann algebras) and noncommutative geometry, with applications to a wide range of areas, including ergodic theory, number theory, representation theory, and mathematical physics.

All talks will be held in Lily Hall, Room 3118. For those driving to campus, we advise you to park in this lot, the Discovery Lot, or the Harrison St Parking Garage. Please be mindful of any parking restrictions that may be in place.

## Program

Titles and abstracts can be viewed here

### Saturday

## 8:30-9:00 | Registration and Coffee

## 9:00-9:45 | Roy Araiza (UIUC): Resource dependent complexity of quantum channels

Motivated by the axiomatic approach to complexity measures introduced by Jaffe, I will present a new resource-dependent complexity measure, and discuss its properties. This complexity measure is flexible in that one is able to apply it to both closed and open systems, and it does not require the resource set to be of any particular form. After discussing our motivation, and some fundamental properties, we will show how by choosing suitable resource sets, we recover the Wasserstein-1 complexity of Jaffe, and also provide lower bounds for Nielsen's geometric complexity. Time allowing, I will also discuss some applications.## 9:55-10:40 | Alejandro Chavez Dominguez (U Oklahoma): Compactness and approximation in operator spaces

Compactness and approximation are two fundamental ideas in analysis which are often intertwined, starting with the basic fact that a compact set in a metric space can be well approximated by a finite set. From the point of view of operator theory in a Hilbert space, an analogous statement would be that any compact operator can be approximated in the operator norm by finite rank operators. Alas, in general Banach spaces this is no longer true and in fact it characterizes the Approximation Property (AP) of Grothendieck. By tweaking a celebrated characterization of compact sets in Banach spaces (also due to Grothendieck) Sinha and Karn defined more restricted notions of compactness, which are associated to weaker approximation properties that are thus enjoyed by more spaces. This is joint with Verónica Dimant and Daniel Glacier.## 10:40-11:10 | Coffee Break

## 11:10-11:55 | Jenny Pi (UCI): How are free entropy and classical entropy related?

Voiculescu introduced two main notions of free entropy for a given tuple of self-adjoint operators \(X\): the microstates free entropy \(\chi(X)\) and the non-microstates free entropy \(\chi^*(X)\). In this talk, we will sketch an elementary proof of the inequality \(\chi(X) \leq \chi^*(X)\) (originally proved using more complex tools by Biane-Capitaine-Guionnet). The proof leverages relationships between the free entropy of a tuple \(X\) and the classical entropy of appropriate matrix approximations to \(X\). This is joint work with David Jekel.## 11:55 | Group Photo!

## 12:00-2:00 | Lunch on your own

~~2:00-2:30 | Arianna Cecco (UH): A Categorical Approach to Injective Envelopes~~(cancelled)

In this talk, I will discuss injectivity and the injective envelopes of objects in different categories. I will present a mix work from my two recent papers, which attempt to answer the question “What happens to injective objects under particular functors?” This is (partially) based on joint work with David Blecher and Mehrdad Kalantar. ## 2:15-3:00 | Daniel Wallick (OSU): Boundary algebras and Kitaev’s quantum double model

Topologically ordered quantum spin systems have become an area of great interest, in part because the ground state space for these systems is a quantum error correcting code. This was reflected in the axiomatization of topological order given by Bravyi, Hastings, and Michalakis. In this talk, we will describe new local topological order axioms given in recent joint work with Corey Jones, Pieter Naaijkens, and David Penneys. These axioms strengthen those of Bravyi, Hastings, and Michalakis, and they give rise to a 1-dimensional net of boundary algebras. We then provide an example satisfying these axioms, namely Kitaev’s quantum double model. We compute the boundary algebras for this model and show that they give nets of algebras either corresponding to Hilb(G) or Rep(G) depending on whether the boundary is rough or smooth. In either case, the inductive limit of the boundary algebras is \(M_{|G|^\infty}\) and we have a canonical state on the boundary algebra which is tracial. This is joint work with Shuqi Wei, Chian Yeong Chuah, David Penneys, Mario Tomba, Brett Hungar, and Kyle Kawagoe.## 3:10-4:55 | Ivan Todorov (UDel): Quantum non-local games and operator space tensor products

The talk will exploit a connection between quantum non-local games and operator space tensor products, discovered by Cooney-Junge-Palazuelos-Perez-Garcia and Regev-Vidick. The values of a quantum non-local game of different types (local, quantum, quantum commuting and no-signalling) will be placed in a unified context, and the quantum commuting value of a quantum game will be identified as the maximal TRO tensor norm of a tensor, canonically associated with the given game. As a consequence, restricting to the local value case, this will lead to a metric characterisation of state convertibility via local operations with shared randomness. The talk will be based on a joint work with Jason Crann, Rupert Levene and Lyudmila Turowska.## 3:55-4:15 | Break

## 4:15-5:00 | Peter Huston (Vanderbilt): Physical applications of systems of commutative algebras in fusion categories

Because of foundational results relating the internal and external Morita theories of fusion categories, algebra objects in fusion categories play many important roles, including in understanding boundaries and phase transitions between topological phases of matter through anyon condensation. In recent joint work with Fiona Burnell and David Penneys, we have used systems of commutative algebras to construct and understand classes of (2+1)D topological defect networks. In this talk, I will describe results related to computing the composition of bimodule categories for fusion categories and bimodule functors, and sketch applications in understanding physical phenomena such as excitations with restricted mobility, symmetry protected topological order, and floquet codes.### Sunday

## 8:30-9:00 | Coffee and networking

## 9:00-9:45 | Brent Nelson (MSU): Ergodic quantum processes on finite von Neumann algebras

Let \((M,\tau)\) be a tracial von Neumann algebra with a separable predual and let \((\Omega, \mathbb{P})\) be a probability space. An ergodic quantum process on \(M\) is a composition of the form \(\gamma_{T^n\omega}\circ \gamma_{T^{n-1}\omega}\circ \cdots \circ \gamma_{T^m\omega}\), where \(\gamma\colon \Omega \times L^1(M,\tau)\to L^1(M,\tau)\) is a bounded positive linear operator, \(T\in \text{Aut}(\Omega, \mathbb{P})\) is ergodic, and \(n,m\in \mathbb{Z}\). Physically, such processes model a discrete time evolution of a quantum system that is subject to (ergodically constrained) disorder. Movassagh and Schenker recently studied ergodic quantum processes in the finite dimensional case \(M=M_n(\mathbb{C})\), and they showed that under reasonable assumptions such processes collapse to rank-one maps on \(L^1(M,\tau)\) exponentially fast almost surely. In this talk, I will discuss how to generalize their results to all separable finite von Neumann algebras. Essential to the analysis in the infinite dimensional case is the so-called Hennion metric on the normal state space of \(M\), which is defined using the natural ordering on \(L^1(M,\tau)_+\). This is based on joint work with Eric B. Roon.## 9:55-10:40 | Adriana Fernandez Quero (UIowa): Rigidity results for group von Neumann algebras with diffuse center

We introduce the first examples of groups \(G\) with infinite center which in a natural sense are recognizable from their von Neumann algebras, \(\mathcal{L}(G)\). Specifically, assume that \(G=A\times G_0\), where \(A\) is an infinite abelian group and \(G_0\) is an ICC wreath-like product group (see Chifan Ioana Osin and Sun, 2023) with property (T), trivial abelianization and torsion free outer automorphism group. Then whenever \(H\) is an*arbitrary*group such that \(\mathcal{L}(G)\) is \(\ast\)-isomorphic to \(\mathcal L(H)\), via an arbitrary \(\ast\)-isomorphism preserving the canonical traces, it must be the case that \(H= B \times H_0\) where \(B\) is infinite abelian and \(H_0\) is isomorphic to \(G_0\). Moreover, we completely describe the \(\ast\)-isomorphism between \(\mathcal L(G)\) and \(\mathcal L(H)\). This yields new applications to the classification of group C\(^*\)-algebras, including examples of non-amenable groups which are recoverable from their reduced C\(^*\)-algebras but not from their von Neumann algebras. This is joint work with Ionut Chifan and Hui Tan.

## 10:40-11:00 | Break

## 11:00-11:45 | Greg Patchell (UCSD): On Sequential Commutation in II1 Factors

We introduce a new Borel equivalence relation on the Haar unitaries of a II1 factor. Two Haar unitaries u and v are related if there exists a finite path of sequentially commuting Haar unitaries in the ultrapower beginning at u and ending at v. Using these commutator paths, we are able to characterize Property Gamma, describe the maximal amenable subalgebras of the free group factors, construct a new exotic non-Gamma II1 factor, and give a strategy for proving the existence of three non-elementarily equivalent non-Gamma II1 factors. This work is joint with Srivatsav Kunnawalkam Elayavalli.## 11:55-12:40 | Therese Landry (UCSB): Spectral Triples for Noncommutative Solenoids

Noncommutative solenoids are inductive limit algebras built from rotation algebras. By viewing noncommutative solenoids as twisted group (C^*)-algebras, we construct spectral triples for noncommutative solenoids based on length functions of bounded doubling. Our spectral triples also induce a Leibniz quantum compact metric space structure. In addition, our spectral triples for noncommutative solenoids are, in the sense of Floricel and Ghorbanpour, likewise inductive limits of spectral triples on rotation algebras. This is joint work with C. Farsi, N. Larsen, and J. Packer.## Registration

Registration is now closed

## Travel Information

Purdue University is located in West Lafayette, Indiana. If traveling by plane, it is recommended you either: (a) fly into Indianapolis Airport (IND) and book a seat on the Lafayette Limo or the Reindeer Shuttle to the PMU; or (b) fly into Chicago O’Hare (ORD) and book either the Lafayette Limo, the Reindeer Shuttle, Express Air Coach. If driving, we advise you to park in this lot, the Discovery Lot, or the Harrison St Parking Garage. Please be mindful of any parking restrictions that may be in place..

## Accomodations

Local options include:

## Local Information

List of dining options, coffee shops, hotels, and other points of interest can be found on this map (toggle options for readabilty):

## Registered Participants

- Abdullah Al Helal, Oklahoma State University
- Roy Araiza, University of Illinois at Urbana-Champaign
- Alejandro Cano, Purdue University
- Arianna Cecco, University of Houston
- Alexandros Chatzinikolaou, University of Delaware, National and Kapodistrian University of Athens
- Alejandro Chavez-Dominguez, University of Oklahoma
- Dominic Cordova, Purdue University
- Marius Dadarlat, Purdue University
- Sayan Das, Embry-Riddle Aeronautical University, Prescott
- Patrick DeBonis, Purdue University
- Juan Felipe Ariza Mejía,The University of Iowa
- Adriana Fernández Quero, University of Iowa
- Felipe Flores, University of Virginia
- David Gao, University of California, San Diego
- Aldo Garcia Guinto, Michigan State University
- Hector Gaxiola Williams, California State University Long Beach
- Colton Griffin, University of Pennsylvania
- Lucas Hall, Michigan State University
- James Harbour, University of Virginia
- Gage Hoefer, University of Delaware
- Peter Huston, Vanderbilt University
- Tania Islam, West Texas A&M University

- David Jekel, Fields Institute
- Ben Jones, Arizona State University
- Ethan Kessinger, Purdue University
- Ajay Kumar Karri, Texas A&M university
- Therese Landry, UCSB
- Yoonkyeong Lee, Michigan State University
- Junhwi Lim, Vanderbilt University
- Kameron McCombs, Dartmouth College
- Iason Moutzouris, Purdue University
- Brent Nelson, Michigan State University
- Micheal O Cobhthaigh, University of Virginia
- Greg Patchell, UC San Diego
- Jenny Pi, UC Irvine
- Eric B. Roon, The University of Arizona
- Vince Ruzicka, University of Wyoming
- Thomas Sinclair, Purdue University
- Arindam Sutradhar, University of Louisiana at Lafayette
- Andrew Toms, Purdue University
- Ivan Todorov, U Del
- Connor Thompson (he/they), Purdue University
- Vincent Villalobos, University of Illinois at Urbana-Champaign
- Daniel Wallick,The Ohio State University
- Hao Wan, Purdue University
- Aoran Wu, University of Virginia
- Junchen Zhao, Texas A&M University

## Acknowledgements

The organizers are grateful for the support from National Science Foundation grants DMS-2035183, DMS-2230405, DMS-2321632, and from Purdue's Department of Mathematics.