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All talks will be held in Cuneo Hall 109

## ECOAS 2016 Schedule:

Saturday, October 1:
Henri Moscovici 9-9:45am
Robin Deeley 10-10:30am
(Coffee Break) 10:30-11am
Elizabeth Gillaspy 12-12:30pm
(Lunch) 12:30-2pm
Vaughan Jones 2-2:45pm
James Tener 3-3:30pm
(Coffee Break) 3:30-4pm
Yungxiang Ren 4-4:30pm
Kate Juschenko 4:45-5:30 pm
(Conference Dinner: 6:30pm
Mt. Everest Restuarant,
630 Church St, Evanston.)

Sunday, October 2:
Ionut Chifan 9-9:45am
Hung-Chang Liao 10-10:30am
(Coffee Break) 10:30-11am
Yasuhiko Sato 11-11:45am
Paul Skoufranis 12-12:45pm

## Abstracts:

Ionut Chifan, "Rigidity in group von Neumann algebra."
Abstract: In the mid thirties F. J. Murray and J. von Neumann found a natural way to associate a von Neumann algebra $L(G)$ to every countable discrete group $G$. Classifying $L(G)$ in terms of $G$ emerged from the beginning as a natural yet quite challenging problem as these algebras tend to have very limited "memory" of the underlying group. This is perhaps best illustrated by Connes' famous result asserting that \emph{all} icc amenable groups give rise to isomorphic von Neumann algebras; thus in this case, besides amenability, the algebra has no recollection of the usual group invariants like torsion, rank, or generators and relations. In the non-amenable case the situation is radically different; many examples where the von Neumann algebraic structure is sensitive to various algebraic group properties have been discovered via Popa's deformation/rigidity theory. In this talk I will present several new instances where the von Neumann algebra completely retains canonical algebraic constructions in group group theory such us direct product, amalgamated free product, or wreath product.

Robin Deeley, "Group actions on Smale spaces and their C*-algebras."
Abstract: I will introduce three examples of Smale spaces (Smale spaces form a class of hyperbolic dynamical system). For each of these examples there are natural Z/2Z and Z-actions. These examples motivate the study of group actions on a general Smale space. I will discuss such actions both in regards to the Smale space itself and the induced action on the C*-algebras associated to it. No knowledge of Smale spaces is required for the talk. This talk is based on joint work with Karen Strung.

Elizabeth Gillaspy,"Irreducible representations of nilpotent groups generate classifiable $C^*$-algebras."
Abstract: In 2015, Eckhardt and McKenney proved that for any finitely generated torsion-free nilpotent group $G$, the $C^*$-algebra $C^*_\pi(G)$ generated by a faithful irreducible representation $\pi$ of $G$ is classifiable by its Elliott invariant. This talk (based on joint work with Caleb Eckhardt) will present the generalization of the Eckhardt-McKenney result to the case of arbitrary finitely generated nilpotent groups, which relies primarily on showing that $C^*_\pi(G)$ satisfies the UCT. Along the way, we also show that $C^*_\pi(G)$ is a cutdown of a twisted group $C^*$-algebra.

Abstract: Zimmer's conjecture states that any action by diffeomorphisms of a lattice (for example Sl_n(Z) ) on a manifold comes from a very nice algebraic action (for example, the natural action of sl_n(Z) in R^n). I'll explain what is this conjecture really about and describe some recent progress on it due to A. Brown, D. Fisher and myself.

Vaughan Jones, "Pythagorean representations of Thompson groups."
Abstract: To each pair A,B of operators on Hilbert space satisfying |A|^2+|B|^2=1 we define Hilbert spaces together with unitary representations of Thompson groups. We look at a few specific examples.

Kate Juschenko, "Cycling amenable groups and soficity"
Abstract: I will give introduction to sofic groups and discuss a possible strategy towards finding a non-sofic group. I will show that if the Higman group were sofic, there would be a map from Z/pZ to itself, locally like an exponential map, satisfying a rather strong recurrence property. The approach to (non)-soficity is based on the study of sofic representations of amenable subgroups of a sofic group. This is joint work with Harald Helfgott.

Hung-Chang Liao, "Rokhlin type theorems for simple nuclear C*-algebras"
Abstract: The classical Rokhlin lemma in ergodic theory asserts that an invertible ergodic measure-preserving transformation on a non-atomic probability space can be approximated by shifts in a suitable sense. In the 1970s, Alain Connes obtained a noncommutative analogue for finite von Neumann algebras, which turns out to be fundamental in understanding the symmetry and structure of injective factors of type II and type III. In this talk, we will discuss the notion of Rokhlin dimension and analogous results for simple nuclear C*-algebras. We will also talk about how these results are related to the nuclear dimension of crossed products and the classification program.

Henri Moscovici, "Primary and secondary invariants of algebras of pseudodifferential symbols."
Abstract: In joint work with A. Gorokhovsky we found the precise cohomological relationship between two canonical constructions (one analytic and the other geometric) of cyclic cocycles on the algebra of complete symbols of pseudodifferential operators. Besides having noteworthy consequences involving invariants of the topological K-theory of the algebra of symbols (of bounded pseudodifferential operators), this leads to the construction of higher regulators on both the relative and the algebraic K-theory of the same algebra.

Yunxiang Ren, "Classification of Thurston-relation subfactor planar algebras."
Abstract: Bisch and Jones suggested the skein theoretic classification of planar algebras and investigated the ones generated by 2-boxes with the second author. In this paper, we consider 3-box generators and classify subfactor planar algebras generated by a non-trivial 3-box satisfying a relation proposed by Thurston. The subfactor planar algebras in the classification are either $E^6$ or the ones from representations of quantum $SU(N)$. We introduce a new method to determine positivity of planar algebras and new techniques to reduce the complexity of computations.

Yasuhiko Sato, "Automorphisms with the Rohlin property on nuclear C*-algebras."
Abstract: In the current study of C*-algebras, there are many branches of the Rohlin property for group actions, the Rohlin property, tracial Rohlin property, Rohlin dimension, and weak Rohlin property. In this talk, we will focus on the difference of such Rohlin properties of automorphisms and try to integrate them in the case of nuclear C*-algebras. Starting from Connes' Rohlin property, we shall see a kind of evolutionary process of Rohlin properties in the C*-algebraic context. In particular, the Rohlin property, introduced by Bratteli-Evans-Kishimoto, is very useful to show the classification theory of dynamical systems. I will also explain the classification of automorphisms in the case of nuclear finite C*-algebras.

Paul Skoufranis, "A Brief Overview of Bi-Free Probability."
Abstract: Recently Voiculescu introduced the notion of bi-free independence as a generalization of free independence in order to simultaneously study the left and right regular representations on free products of vector spaces. In this talk, we will provide a brief overview of the current state of bi-free probability. This overview will include basic definitions, bi-free cumulants, bi-free infinitely divisible distributions, operator-valued bi-free independence, bi-free matrix models, and bi-free partial transformations.

James Tener, "Geometric construction of conformal nets."
Abstract: Conformal nets are families of III_1 factors indexed by intervals on a circle. In this talk, I'll outline a construction of conformal nets in the spirit of Segal's geometric formalism for conformal field theory involving linear maps assigned to Riemann surfaces with boundary. Time permitting, I will also discuss applications to the construction of finite index subfactors.