 Joachim Cuntz (Muenster)
 James
Glimm (SUNY Stonybrook)
 Nigel
Higson (Penn State)
 Arthur Jaffe (Harvard)
 Vaughan Jones (Vanderbilt)
 Charles Kane (Penn)
 Magdalena Musat (Copenhagen)
 Emil Prodan (Yeshiva)
 Marc Rieffel (Berkeley)
 Erik Van Erp (Dartmouth)
 Dan Voiculescu (Berkeley)
Schedule (subject to change)
All talks will take place in the Auditorium 1 of the David Rittenhouse Laboratories (DRL A1), see the Home tab above for a map.
In the schedule below, click on the speaker's name for the title and abstract of their talk
SaturdayMarch 30 

8:00  9:00  Registration / Refreshments 
9:00  9:15  Opening remarks 
9:15  10:00  Vaughan F.R. Jones 
10:00  10:30  Coffee break 
10:30  11:15  Joachim Cuntz 
11:15  12:00  James Glimm 
12:00  2:00  Lunch break 
2:00  2:45  Charles Kane 
2:45  3:30  Emil Prodan 
3:30  4:00  Coffee break 
4:00  4:45  Erik Van Erp 
4:45  5:30  Short presentations 
6:00  8:00  Banquet (at SangKee Noodle House  3549 Chestnut Street) 
SundayMarch 31 

8:00  9:00  Coffee and light breakfast 
9:009:45  Nigel Higson 
9:45  10:15  Coffee break 
10:15  11:00  Marc Rieffel 
11:00  11:45  Dan Voiculescu 
12:00  2:00  Lunch break 
2:00  2:45  Magdelena Musat 
2:45  3:30  Arthur Jaffe 
3:30  4:00  Coffee break 
4:00  4:30  Short presentations 
4:30  5:30  Panel discussion on Operator
Algebras in the twentyfirst century Panelists: Paul Baum, Nigel Higson and Vaughan Jones Moderator: Jonathan Block 
Abstracts
Joachim Cuntz (Muenster)
"The ring of integers and C*algebras"
Among the most basic structures in mathematics are the sets of natural numbers and of integers with their operations of addition and multiplication. These structures give rise, in a completely natural way, to C*algebras with intriguing properties. The study of these C*algebras and in particular of their Ktheoretical invariants reveals close connections with algebraic number theory. These connections can be extended, from the usual ring of integers to rings of algebraic integers in number fields.
Jim Glimm (SUNY Stonybrook)
"Mathematical Theories for Turbulent Flow"
1. We address a long standing controversy in statistical
physics: Extensions of the 2nd law of thermodynamics to dynamic
phenomena. The 2nd law states that entropy is constant or increases.
This is not a dynamic law. Consequences of the extension for numerical
methods are explored.
2. Solutions of the Euler equation exist and with specified regularity,
assuming K41 as a hypothesis. For two fluid mixing, the regularity is
much weaker and is formulated in terms of measure valued (Youngs
measure) solutions.
Nigel Higson (Penn State)
"C*algebras and tempered representations"
The theory of unitary group representations featured prominently in the work of the functional analysis group at Penn (although less prominently in the work of Dick Kadison himself). In this talk I shall focus on HarishChandra’s theory of tempered representations for reductive Lie groups. Even though functional analysis played an essential role in formulating the problem that HarishChandra eventually solved in his life’s work, it didn’t feature prominently in the solution itself. But I shall try to explain how perspectives from Alain Connes’ noncommutative geometry suggest new roles for functional analysis, particularly C*algebra theory, in recasting of HarishChandra’s work.
Arthur Jaffe (Harvard)
"The story behind the Millennium Prize Problems in Mathematics"
In May 2000, seven mathematical questions were announced as Millennium Prize Problems. We recount the “back story” history of how this came about and what followed.
Vaughan Jones (Vanderbilt)
"Subfactors from Penn on"
Kadison reigned king of operator algebras at Penn in 1981 when subfactor theory began, at Penn. After a few reminiscences about the early days I will describe some of the twists and turns taken by the theory, including significant interactions with topology and physics, and a recent construction of unitary representations of some groups of homeomorphism groups of the circle.
Charles Kane (Penn)
"Topological Quantum Matter"
Mathematical constructions in topology have had a profound impact on our understanding of quantum phases of matter. This has helped to inspire the discoveries of new classes of electronic materials that have important implications for both fundamental science and technology. We will describe these developments and the role that topological invariants, characteristic classes and ChernSimons theory have played in them.
Magdelena Musat (Copenhagen)
"Von Neumann Algebras meet Quantum Information Theory"
The study of quantum correlations arising under two different assumptions of commutativity of observables, initiated by Tsirelson in the 80’s, has proven over the last decade to have deep interconnections with important problems in operator algebras theory, including various reformulations of the Connes Embedding Problem. In very recent work with M. Rørdam, we show that in every dimension n > 11, the set of n x n matrices of correlations arising from unitaries in finite dimensional von Neumann algebras is not closed. As a consequence, in each such dimension there are quantum channels that admit type II_{1}von Neumann algebras as ancillas, but not finite dimensional ones, thus witnessing new infinite dimensional phenomena in quantum information theory.
Emil Prodan (Yeshiva)
"New directions in materials science guided by research in operator algebras"
Operator algebras are best known to physicists through their applications in quantum field theory and statistical physics. Recently, however, operator algebras have found outstanding applications in materials science, leading to a deeper understanding of known materials as well as to discovery of entirely new classes of materials. This lecture will focus on metamaterials built with the socalled bulkboundary principle in mind. As we shall see, the latter is related to the topology of the spectra of elements from a C*algebra and to how the topological types of the spectra are modified by extensions of that algebra. Examples where this type of questions can be entirely or partially answered with tools from Ktheory/indextheory will be analyzed (they are drawn from noncommutative tori, discrete crossed products and certain grupoid algebras). The physical manifestation of these results will be exemplified using computer simulations and experimental measurements. Furthermore, some of these examples have been already engineered into metamaterials supporting unique waveguiding modes along the boundaries or interfaces, and these accomplishments will be reviewed during the presentation.
Marc Rieffel (UC Berkeley)
"Progress on quantum metric spaces"
I will briefly give the definition of a compact quantum metric space, and then describe a few of the growing number of examples. I will then discuss the evolution of the definition of quantum GromovHausdorff distance. I will indicate some of the connections with physics, involving quantum vector bundles and Dirac operators.
Erik van Erp (Dartmouth)
"The Heisenberg calculus and cyclic cohomology"
Epstein and Melrose investigated the Fredholm index problem for hypoelliptic
operators in the Heisenberg calculus on contact manifolds. They placed the problem
in the context of Hochschild cohomology. We revisit this program by studying the
index map in the context of cyclic cohomology. This is joint work with Alexander
Gorokhovsky.
DanVirgil Voiculescu (UC Berkeley)
"A hydrodynamic exercise in free probability: free Euler equations"
For the free probability analogue of Euclidean space endowed with the Gaussian measure, which is the context of the von Neumann algebra of a free group, we apply the approach of Arnold to derive Euler equations for a Lie algebra of of noncommutative vector fields which preserve a certain trace. We extend the equations to vector fields satisfying noncommutative smoothness requirements. We also introduce a cyclic vorticity and show that it satisfies certain vorticity equations and that it produces a family of conserved quantities.
Saturday Short Presentations:
4:45 Nayak Soumyashant (Penn)
"Rank identities and determinant identities in operator algebras"
5:00 Evangelos Nastas (Florida Atlantic U)
"Coadjoint Representation Invariants of Lie algebras in low dimension"
5:15 Vrej Zarikian (US Naval Academy)
"The Pure Extension Property for Discrete Crossed Products"
Sunday Short Presentations:
4:00 Alexander A. Katz (St. John's University)
"On the local structure in operator algebras"