# Program and Abstracts

All talks are in Clark Hall Room 107 on the University of Virginia Campus.

8:15 – 9:00

Coffee and continental breakfast in Clark Hall.

9:00 – 9:45

Michael Hartz (Washington University in St. Louis)

A multiplier functional calculus

Abstract: A classical result of Sz.-Nagy and Foias shows that every contraction $T$ on a Hilbert space without unitary summand admits an $H^\infty$-functional calculus, that is, one can make sense of $f(T)$ for every bounded analytic function $f$ in the unit disc.

I will talk about a generalization of this result, which applies to tuples of commuting operators and multiplier algebras of a large class of Hilbert function spaces on the unit ball. In particular, this extends a recent theorem of Clou\^atre and Davidson for commuting row contractions. This is joint work with Kelly Bickel and John McCarthy.

10:00 – 10:45

Florent Baudier (Texas A&M University)

Banach Spaces and Graphs: Geometric Interactions and Applications.

Abstract: The embeddability of a graph into a Banach space says much about the graph, but also about the Banach space itself. The embeddability theory of metric spaces has far reaching applications in theoretical computer science, geometric group theory, noncommutative geometry and topology. We will discuss a few of them before elaborating on the interaction between the geometry of non-locally finite graphs and the asymptotic structure of Banach spaces. In particular, we will show how this approach was recently used to solve the problem of the coarse minimality of Hilbert space.

11:00 – 11:45

Sarah Reznikoff (Kansas State University)

Title: Renault’s groupoid for the abelian core

Graph algebras and generalizations have provided a wealth of examples of C*-algebras with underlying combinatorial structure.   Uniqueness theorems have been central to the analysis of these algebras. Recent generalized uniqueness theorems identify a salient C*-subalgebra, the cycline subalgebra, from which injectivity of a representation lifts.  We will describe this subalgebra and new work on the corresponding Weyl groupoid.

11:50 – 2:00

Lunch. We will provide a map with a variety of restaurants within walking distance, and we will lead groups to different places.

2:00 – 2:45

Christian Rosendal (University of Illinois – Chicago)

Affine isometric actions and the geometry of Polish groups

Abstract: We will present a number of results relating the geometry of Polish groups with the geometry of Banach spaces on which they act by affine isometries.

3:00 – 3:45

George Androulakis (University of South Carolina)

Several forms of chaos in quantum mechanics

Abstract:  We present several forms of chaos that arise in quantum mechanics.We indicate relationships between them and discuss how they can be measured.

4:00 – 4:45

Nik Weaver (Washington University in St. Louis)

A “quantum” Ramsey theorem for operator systems

Abstract: Let $V$ be a linear subspace of $M_n(C)$ which contains the identity and is stable under the formation of Hermitian adjoints. I claim that if n is sufficiently large then there exists a rank k orthogonal projection such that $dim(PVP) = 1$ or $k^2$. I will explain the relationship between this result and the classical theorem of Ramsey about finite graphs,and also discuss its origin in the theory of quantum error correction.