Videos and presentation materials from other INI events are also available.
Event  When  Speaker  Title  Presentation Material 

OASW04 
11th January 2017 13:30 to 15:00 
David Penneys 
Introduction to subfactor theory
In this series of lectures, I'll give an introduction to the modern
theory of subfactors initiated by Vaughan Jones. We'll begin with invariants
for subfactors, like the index, the principal graph, and the standard
invariant. We'll then discuss Jones' planar algebras as an elegant and
powerful tool for the construction and classification of subfactors. The
standard invariant can also be seen as a unitary 2category, and the
categorical framework has been very important for recent results.
Finally, we'll discuss the classification of 'small' examples from several
viewpoints.


OASW04 
11th January 2017 15:00 to 16:30 
Yasu Kawahigashi 
Subfactors, tensor categories and conformal field theory
I
will give introductory discussions on type III factors, the
TomitaTakesaki
theory, type III subfactors, tensor categories,
braiding,
quantum doubles, alphainduction and local conformal nets.


OASW04 
12th January 2017 13:30 to 15:00 
David Penneys 
Introduction to subfactor theory
In this series of lectures, I'll give an introduction to the modern
theory of subfactors initiated by Vaughan Jones. We'll begin with invariants
for subfactors, like the index, the principal graph, and the standard
invariant. We'll then discuss Jones' planar algebras as an elegant and
powerful tool for the construction and classification of subfactors. The
standard invariant can also be seen as a unitary 2category, and the
categorical framework has been very important for recent results.
Finally, we'll discuss the classification of 'small' examples from several
viewpoints.


OASW04 
12th January 2017 15:00 to 16:30 
Yasu Kawahigashi 
Subfactors, tensor categories and conformal field theory
I
will give introductory discussions on type III factors, the
TomitaTakesaki
theory, type III subfactors, tensor categories,
braiding,
quantum doubles, alphainduction and local conformal nets.


OASW04 
13th January 2017 13:30 to 15:00 
David Penneys 
Introduction to subfactor theory
In this series of lectures, I'll give an introduction to the modern
theory of subfactors initiated by Vaughan Jones. We'll begin with invariants
for subfactors, like the index, the principal graph, and the standard
invariant. We'll then discuss Jones' planar algebras as an elegant and
powerful tool for the construction and classification of subfactors. The
standard invariant can also be seen as a unitary 2category, and the
categorical framework has been very important for recent results.
Finally, we'll discuss the classification of 'small' examples from several
viewpoints.


OASW04 
13th January 2017 15:00 to 16:30 
Yasu Kawahigashi 
Subfactors, tensor categories and conformal field theory
I
will give introductory discussions on type III factors, the
TomitaTakesaki
theory, type III subfactors, tensor categories,
braiding,
quantum doubles, alphainduction and local conformal nets.


OASW04 
16th January 2017 13:30 to 15:00 
David Penneys 
Introduction to subfactor theory
In this series of lectures, I'll give an introduction to the modern
theory of subfactors initiated by Vaughan Jones. We'll begin with invariants
for subfactors, like the index, the principal graph, and the standard
invariant. We'll then discuss Jones' planar algebras as an elegant and
powerful tool for the construction and classification of subfactors. The
standard invariant can also be seen as a unitary 2category, and the
categorical framework has been very important for recent results.
Finally, we'll discuss the classification of 'small' examples from several
viewpoints.


OASW04 
16th January 2017 15:00 to 16:30 
Yasu Kawahigashi 
Subfactors, tensor categories and conformal field theory
I
will give introductory discussions on type III factors, the
TomitaTakesaki
theory, type III subfactors, tensor categories,
braiding,
quantum doubles, alphainduction and local conformal nets.


OASW04 
17th January 2017 13:30 to 15:00 
Roberto Longo  Operator Algebras and Conformal Field Theory  
OASW04 
17th January 2017 15:00 to 16:30 
Stefaan Vaes 
Representation theory, cohomology and L^2Betti numbers for subfactors
The
standard invariant of a subfactor can be viewed in
different
ways as a ``discrete group like'' mathematical structure  a
lambdalattice
in the sense of Popa, a Jones planar algebra, or a
C*tensor
category of bimodules. This discrete group point of view
will
be the guiding theme of the mini course. After an introduction to
different
approaches to the standard invariant, I will present joint
work
with Popa and Shlyakhtenko on the unitary representation theory of
these
structures, on approximation and rigidity properties like
amenability,
the Haagerup property or property (T), on (co)homology and
$L^2$Betti
numbers. I will present several examples and also discuss a
number
of open problems on the realization of standard invariants
through
hyperfinite subfactors.


OASW04 
18th January 2017 09:00 to 10:30 
Roberto Longo  Operator Algebras and Conformal Field Theory  
OASW04 
18th January 2017 10:30 to 12:00 
Stefaan Vaes 
Representation theory, cohomology and L^2Betti numbers for subfactors
The
standard invariant of a subfactor can be viewed in
different
ways as a ``discrete group like'' mathematical structure  a
lambdalattice
in the sense of Popa, a Jones planar algebra, or a
C*tensor
category of bimodules. This discrete group point of view
will
be the guiding theme of the mini course. After an introduction to
different
approaches to the standard invariant, I will present joint
work
with Popa and Shlyakhtenko on the unitary representation theory of
these
structures, on approximation and rigidity properties like
amenability,
the Haagerup property or property (T), on (co)homology and
$L^2$Betti
numbers. I will present several examples and also discuss a
number
of open problems on the realization of standard invariants
through
hyperfinite subfactors.


OASW04 
19th January 2017 13:30 to 15:00 
Roberto Longo  Operator Algebras and Conformal Field Theory  
OASW04 
19th January 2017 15:00 to 16:30 
Stefaan Vaes 
Representation theory, cohomology and L^2Betti numbers for subfactors
The
standard invariant of a subfactor can be viewed in
different
ways as a ``discrete group like'' mathematical structure  a
lambdalattice
in the sense of Popa, a Jones planar algebra, or a
C*tensor
category of bimodules. This discrete group point of view
will
be the guiding theme of the mini course. After an introduction to
different
approaches to the standard invariant, I will present joint
work
with Popa and Shlyakhtenko on the unitary representation theory of
these
structures, on approximation and rigidity properties like
amenability,
the Haagerup property or property (T), on (co)homology and
$L^2$Betti
numbers. I will present several examples and also discuss a
number
of open problems on the realization of standard invariants
through
hyperfinite subfactors.


OASW04 
20th January 2017 09:00 to 10:30 
Roberto Longo  Operator Algebras and Conformal Field Theory  
OASW04 
20th January 2017 10:30 to 12:00 
Stefaan Vaes 
Representation theory, cohomology and L^2Betti numbers for subfactors
The
standard invariant of a subfactor can be viewed in
different
ways as a ``discrete group like'' mathematical structure  a
lambdalattice
in the sense of Popa, a Jones planar algebra, or a
C*tensor
category of bimodules. This discrete group point of view
will
be the guiding theme of the mini course. After an introduction to
different
approaches to the standard invariant, I will present joint
work
with Popa and Shlyakhtenko on the unitary representation theory of
these
structures, on approximation and rigidity properties like
amenability,
the Haagerup property or property (T), on (co)homology and
$L^2$Betti
numbers. I will present several examples and also discuss a
number
of open problems on the realization of standard invariants
through
hyperfinite subfactors.


OASW01 
23rd January 2017 10:00 to 11:00 
Sorin Popa 
On rigidity in II1 factor framework
II1 factors appear naturally from a multitude of data (groups, group actions, operations such as free products, etc). This leads to two types of rigidity phenomena in this framework: 1. W*rigidity, aiming at recovering the building data from the isomorphism class of the algebra. 2. Restrictions on the symmetries of the II1 factor (like the index of its subfactors). We will discuss some old and new results in this direction, and the role of deformationrigidity techniques in obtaining them. 

OASW01 
23rd January 2017 11:30 to 12:30 
Stephen Bigelow 
A diagrammatic approach to Ocneanu cells
Kuperberg's SU(3) spider has "web" diagrams with oriented strands and trivalent vertices. A closed web evaluates to a real number, which can be thought of as a weighted sum of certain ways to "colour" the faces of the web. The weighting here is defined using Ocneanu cells, which were explicitly calculated in a 2009 paper by Evans and Pugh. I will describe a diagrammatic way to recover their calculation in the simplest case of the A series. Each strand of a web becomes a parallel pair of coloured strands, and each vertex becomes three coloured strands that connect up the three incoming pairs of coloured strands. 

OASW01 
23rd January 2017 13:30 to 14:30 
Corey Jones 
Operator Algebras in rigid C*tensor categories
In this talk, we will describe a theory of operator algebra objects in an arbitrary rigid C*tensor category C. Letting C be the category of finite dimensional Hilbert spaces, we recover the ordinary theory of operator algebras. We will explain the philosophy and motivation for this framework, and how it provides a unified perspective on various aspects of the theories of rigid C*tensor categories, quantum groups, and subfactors. This is based on joint work with Dave Penneys.


OASW01 
23rd January 2017 14:30 to 15:30 
David Jordan 
Dualizability and orientability of tensor categories
A topological field theory is an invariant of oriented manifolds, valued in some category C, with many pleasant properties. According to the cobordism hypothesis, a fully extended  a.k.a. fully local  TFT is uniquely determined by a single object of C, which we may think of as the invariant assigned by the theory to the point. This object must have strong finiteness properties, called dualizability, and strong symmetry properties, called orientability. In this talk I'd like to give an expository discussion of several recent works "in dimension 1,2, and 3"  of SchommerPries, DouglasSchommerPriesSnyder, BrandenburgChivrasituJohnsonFreyd, CalaqueScheimbauer  which unwind the abstract notions of dualizability and orientability into notions very familiar to the assembled audience: things like Frobenius algebras, fusion categories, pivotal fusion categories, modular tensor categories. Finally in this context, I'll discuss some work in progress with Adrien Brochier and Noah Snyder, which finds a home on these shelves for arbitrary tensor and pivotal tensor categories (no longer finite, or semisimple), and for braided and ribbon braided tensor categories. 

OASW01 
23rd January 2017 16:00 to 17:00 
Yusuke Isono 
On fundamental groups of tensor product II_1 factors
We study a stronger notion of primeness for II_1 factors, which was
introduced in my previous work. Using this, we prove that if G and H are
groups which are realized as fundamental groups of II_1 factors, then
so are groups GH and G \cap H.


OASW01 
24th January 2017 10:00 to 11:00 
George Elliott 
The classification of unital simple separable C*algebras with finite nuclear dimension
As, perhaps, a climax to forty years of work by many
people,
the class of algebras in the title (assumed also to
satisfy the UCT, which
holds in all concrete examples and may be automatic) can
now be classified
by means of elementary invariants (the Kgroups
and tracial simplex).


OASW01 
24th January 2017 11:30 to 12:30 
Stuart White 
The structure of simple nuclear C*algebras: a von Neumann prospective
I'll discuss aspects of structure of simple nuclear C*algebras ( in particular the TomsWinter regularity conjecture) drawing parallels with results for injective von Neumann algebras. 

OASW01 
24th January 2017 13:30 to 14:30 
Wilhelm Winter 
Structure and classification of nuclear C*algebras: The role of the UCT
The question whether all separable nuclear C*algebras satisfy the Universal Coefficient Theorem remains one of the most important open problems in the structure and classification theory of such algebras. It also plays an integral part in the connection between amenability and quasidiagonality. I will discuss several ways of looking at the UCT problem, and phrase a number of intermediate questions. This involves the existence of Cartan MASAS on the one hand, and certain kinds of embedding problems for strongly selfabsorbing C*algebras on the other. 

OASW01 
24th January 2017 14:30 to 15:30 
Sam Evington 
W$^*$Bundles and Continuous Families of Subfactors
W$^*$bundles were first introduced by Ozawa, motivated by work on the TomsWinter Conjecture and, more generally, the classification of C$^*$algebras. I will begin with a brief introduction to W$^*$bundles, explaining how they combine the measure theoretic nature of tracial von Neumann algebras with the topological nature of C$^*$algebras. I will then discuss the relationship between the triviality problem for W$^*$bundles and the TomsWinter Conjecture. Finally, I will present my work with Ulrich Pennig on locally trivial W$^*$bundles and my ongoing work on expected subbundles of W$^*$bundles inspired by subfactor theory. 

OASW01 
24th January 2017 16:00 to 17:00 
Koichi Shimada 
A classification of realline group actions with faithful ConnesTakesaki modules on hyperfinite factors
We classify certain reallinegroup actions on (type III) hyperfinite factoers, up to cocycle conjugacy. More precisely, we show that an invariant called the ConnesTakesaki module completely distinguishs actions which are not approximately inner at any nontrivial point. Our classification result is related to the uniqueness of the hyperfinite type III_1 factor, shown by Haagerup, which is equivalent to the uniquness of reallinegroup actions with a certain condition on the hyperfinite type II_{\infty} factor. We classify actions on hyperfinite type III factors with an analogous condition. The proof is based on MasudaTomatsu's recent work on reallinegroup actions and the uniqueness of the hyperfinite type III_1 factor. 

OASW01 
25th January 2017 10:00 to 11:00 
Stefaan Vaes 
Classification of free ArakiWoods factors
Coauthors: Cyril Houdayer (Université Paris Sud) and Dimitri Shlyakhtenko (UCLA). Free ArakiWoods factors are a free probability analog of the type III hyperfinite factors. They were introduced by Shlyakhtenko in 1996, who completely classified the free ArakiWoods factors associated with almost periodic orthogonal representations of the real numbers. I present a joint work with Houdayer and Shlyakhtenko in which we completely classify a large class of non almost periodic free ArakiWoods factors. The key technical result is a deformation/rigidity criterion for the unitary conjugacy of two faithful normal states on a von Neumann algebra. 

OASW01 
25th January 2017 11:30 to 12:30 
Dima Shlyakhtenko 
Cohomology and $L^2$Betti numbers for subfactors and quasiregular inclusions
Coauthors: Sorin Popa (UCLA) and Stefaan Vaes
(Leuven) We introduce L$^2$Betti numbers, as well as a general homology and cohomology theory for the standard invariants of subfactors, through the associated quasiregular symmetric enveloping inclusion of II$_1$ factors. We actually develop a (co)homology theory for arbitrary quasiregular inclusions of von Neumann algebras. For crossed products by countable groups Γ, we recover the ordinary (co)homology of Γ. For Cartan subalgebras, we recover Gaboriau's L$^2$Betti numbers for the associated equivalence relation. In this common framework, we prove that the L$^2$Betti numbers vanish for amenable inclusions and we give cohomological characterizations of property (T), the Haagerup property and amenability. We compute the L$^2$Betti numbers for the standard invariants of the TemperleyLiebJones subfactors and of the FussCatalan subfactors, as well as for free products and tensor products. 

OASW01 
25th January 2017 13:30 to 14:30 
Arnaud Brothier 
Crossedproducts by locally compact groups and intermediate subfactors.
I will present examples of an action of a totally disconnected group G on a factor Q such that intermediate subfactors between Q and the crossedproduct correspond to closed subgroups of G. This extends previous work of Choda and IzumiLongoPopa. I will discuss about the analytical difference with the case of actions of discrete groups regarding the existence of conditional expectations or operator valued weights. Finally I will talk about intermediate subfactors in the context of actions of Hecke pairs of groups. This is a joint work with Rémi Boutonnet.


OASW01 
25th January 2017 14:30 to 15:30 
Alexei Semikhatov  Screening operators in conformal field models and beyond  
OASW01 
25th January 2017 16:00 to 17:00 
Alice Guionnet  tba  
OASW01 
26th January 2017 10:00 to 11:00 
Benjamin Doyon 
Conformal field theory out of equilibrium
Nonequilibrium conformal field theory is the application of methods of conformal field theory to states that are far from equilibrium. I will describe exact results for currentcarrying steadystates that occur in the partitioning protocol: two baths (halflines) are independently thermalized at different temperatures, then joined together and let to evolve for a large time. Results include the exact energy current, the exact scattering map describing steadystate averages and correlations of all fields in the energy sector (the stressenergy tensor and its descendants), and the full scaled cumulant generating function describing the fluctuations of energy transport. I will also explain how, in spacetime, the steady state occurs between contact discontinuities beyond which lie the asymptotic baths. If time permits, I will review how these results generalize to higherdimensional conformal field theory, and to nonconformal integrable models. This is work in collaboration with Denis Bernard.


OASW01 
26th January 2017 11:30 to 12:30 
Alina Vdovina 
Buildings and C*algebras
We will give an elementary introduction to the theory of buildingsfrom a geometric point of view. Namely, we present buildings as universal coversof finite polyhedral complexes. It turns out that the combinatorial structure of these complexesgives rise to a large class of higher rank CuntzKrieger algebras, which Ktheory can be explicitly computed.


OASW01 
26th January 2017 13:30 to 14:30 
Claus Kostler 
An elementary approach to unitary representations of the Thompson group F
I provide an elementary construction of unitary representations of the Thompson group
F. Further I will motivate this new
approach by recent results on distributional symmetries in noncommutative
probability. My talk is based on joined
work with Rajarama Bhat, Gwion Evans, Rolf Gohm and Stephen Wills.


OASW01 
26th January 2017 14:30 to 15:30 
Rolf Gohm 
Braids, Cosimplicial Identities, Spreadability, Subfactors
Actions of a braid monoid give rise to cosimplicial identities. Cosimplicial identities for morphisms of (noncommutative) probability spaces lead to spreadable processes for which there is a (noncommutative) de Finetti type theorem. This scheme can be applied to braid group representations from subfactors. We discuss results and open problems of this approach. This is joint work with G. Evans and C. Koestler.


OASW01 
26th January 2017 16:00 to 17:00 
Alexei Davydov 
Modular invariants for grouptheoretical modular data
Grouptheoretical modular categories is a class of modular categories
for which modular invariants can be described effectively (in
grouptheoretical terms). This description is useful for applications in
conformal field theory, allowing classification of full CFTs with given
chiral halves being holomorphic orbifolds. In condensed matter physics
it can be used to classify possible boson condensations. It also
provides ways of studying braided equivalences between grouptheoretical
modular categories.
The class of modular categories can be used to provide examples of
counterintuitive behaviour of modular invariants: multiple physical
realisations of a given modular invariant, nonphysicality of some
natural modular invariants.
The talk will try to give an overview of known results and open
problems.


OASW01 
27th January 2017 10:00 to 11:00 
Julia Plavnik 
On gauging symmetry of modular categories
Coauthors: Shawn X. Cui
( Stanford University), César Galindo
(Universidad de los Andes), Zhenghan Wang
(Microsoft Research, Station QUniversity of CaliforniaSanta Barbara)
A very interesting class of fusion categories is the one formed by modular categories. These categories arise in a variety of mathematical subjects including topological quantum field theory, conformal field theory, representation theory of quantum groups, von Neumann algebras, and vertex operator algebras. In addition to the mathematical interest, a motivation for pursuing a classification of modular categories comes from their application in condensed matter physics and quantum computing. Gauging is a wellknown theoretical tool to promote a global symmetry to a local gauge symmetry. In this talk, we will present a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a unitary modular category (UMC) with a symmetry group G, gauging is a 2step process: first extend the UMC to a Gcrossed braided fusion category and then take the equivariantization of the resulting category. This is an useful tool to construct new modular categories from given ones. We will show through concrete examples which are the ingredients involved in this process. In addition, if time allows, we will mention some classification results and conjectures associated to the notion of gauging. 

OASW01 
27th January 2017 11:30 to 12:30 
Pinhas Grossman 
Algebras, automorphisms, and extensions of quadratic fusion categories
To a finite index subfactor there is a associated a tensor category along with a distinguished algebra object. If the subfactor has finite depth, this tensor category is a fusion category. The BrauerPicard group of a fusion category, introduced by EtingofNikshychOstrik, is the (finite) group of Morita autoequivalences. It contains as a subgroup the outer automorphism group of the fusion category. In this talk we will decribe the BrauerPicard groups of some quadratic fusion categories as groups of automorphisms which move around certain algebra objects. Combining this description with an operator algebraic construction, we can classify graded extensions of the AsaedaHaagerup fusion categories. This is joint work with Masaki Izumi and Noah Snyder. 

OASW01 
27th January 2017 13:30 to 14:30 
Noah Snyder 
Trivalent Categories
If N


OASW01 
27th January 2017 14:30 to 15:30 
Henry Tucker 
Eigenvalues of rotations and braids in spherical fusion categories
Coauthors: Daniel Barter (University of Michigan), Corey Jones (Australian National University) Using the generalized categorical FrobeniusSchur indicators for semisimple spherical categories we have established formulas for the multiplicities of eigenvalues of generalized rotation operators. In particular, this implies for a finite depth planar algebra, the entire collection of rotation eigenvalues can be computed from the fusion rules and the traces of rotation at finitely many depths. If the category is also braided these formulas yield the multiplicities of eigenvalues for a large class of braids in the associated braid group representations. This provides the eigenvalue multiplicities for braids in terms of just the S and T matrices in the case where the category is modular. Related Links


OASW01 
27th January 2017 16:00 to 17:00 
David Penneys 
Operator algebras in rigid C*tensor categories, part II
In this talk, we will first define a (concrete) rigid C*tensor category. We will then highlight the main features that are important to keep in mind when passing to the abstract setting. I will repeat a fair amount of material on C*/W* algebra objects from Corey Jones' Monday talk. Today's goal will be to prove the GelfandNaimark theorem for C*algebra objects in Vec(C). To do so, we will have to understand the analog of the W*algebra B(H) as an algebra object in Vec(C). In the remaining time, we will elaborate on the motivation for the project from the lens of enriched quantum symmetries. This talk is based on joint work with Corey Jones (arXiv:1611.04620). 

OAS 
31st January 2017 15:30 to 16:30 
Scott Morrison 
The TemperleyLieb category in operator algebras and in link homology
The TemperleyLieb category appears in a fundamental way in both the
study of subfactors and in link homology theories. Indeed, the discovery of the
importance of the TemperleyLieb category for subfactors led to the creation of
the Jones polynomial, and thence, after a long gestation, Khovanov homology.


OAS 
7th February 2017 14:00 to 15:00 
Yoh Tanimoto 
Free products in AQFT
We apply the free product construction to various local algebras in
algebraic quantum field theory. If we take the free product of infinitely many identical irreducible halfsided modular inclusions, we obtain a halfsided modular inclusion with ergodic canonical endomorphism and trivial relative commutant. On the other hand, if we take finitely many Moebius covariant nets with trace class property, we are able to construct an inclusion of free product von Neumann algebras with a large relative commutant. (joint work with R. Longo and Y. Ueda) 

OAS 
9th February 2017 14:00 to 15:00 
Vincenzo Morinelli 
Conformal covariance and the split property
Several important structural properties of a quantum field theory are
known to be automatic in the conformal case. The split property is the statistical
independence of local algebras associated to regions with a positive
(spacelike) separation. We show that in chiral theories when the full conformal
(i.e. diffeomorphism) covariance is assumed, then the split property holds.
Time permitting, we also provide an example of a twodimensional conformal net
that does not have the split property. The talk relies on the joint work "Conformal covariance and the split property" with Y. Tanimoto (Uni. of Rome "Tor Vergata"), M. Weiner (Budapest Uni. of Technology and Economics), arXiv:1609.02196. 

OAS 
14th February 2017 14:00 to 15:00 
Masaki Izumi 
Indecomposable characters of infinite dimensional groups associated with operator algebras
A character of a topological group is a normalized
continuous positive definite class function on the group. I'll give an account
of recent classification results on characters of infinite dimensional groups
associated with operator algebras, including the unitary groups of unital
simple AF algebras and II_1 factors. 

OAS 
16th February 2017 14:00 to 15:00 
Stefano Rossi 
Endomorphisms and automorphisms of the 2adic ring C*algebra Q_2
The 2adic ring C*algebra is the universal C*algebra Q_2 generated by
an isometry S_2 and a unitary U such that S_2U=U^2S_2 and
S_2S_2^*+US_2S_2^*U^*=1. By its very definition it contains a copy of the
Cuntz algebra O_2. I'll start by discussing some nice properties of this inclusion,
as they came to be pointed out in a recent joint work with V. Aiello
and R. Conti. Among other things, the inclusion enjoys a kind of rigidity
property, i.e., any endomorphism of the larger that restricts trivially to the smaller must
be trivial itself. I'll also say a word or two about the extension problem,
which is concerned with extending an endomorphism of O_2 to an endomorphism of
Q_2. As a matter of fact, this is not always the case: a wealth of examples
of nonextensible endomorphisms (automophisms indeed!) show up as soon as
the socalled Bogoljubov automorphisms of O_2 are looked at. Then
I'll move on to particular classes of endomorphisms and automorphisms of
Q_2, including those fixing the diagonal D_2. Notably,
the semigroup of the endomorphisms fixing U turns out to be a maximal
abelian group isomorphic with the group of continuous functions from
the onedimensional torus to itself. Such an analysis, though, calls for
some knowledge of the inner structure of Q_2. More precisely, it's vital
to prove that C*(U) is a maximal commutative subalgebra. Time permitting,
I'll also try to present forthcoming generalizations to broader
classes of C*algebras, on which we're currently working with N. Stammeier
as well. 

OAS 
21st February 2017 14:00 to 15:00 
Denjoe O'Connor 
Membrane Matrix Models and nonperturbative tests of gauge/gravity
I will review how relativistic membranes lead to membrane matrix models and compare nonperturbative studies of some of these matrix models with results from gravitational predictions. The principal models of interest will be the BFSS, BMN and BerkoozDouglas models. 

OAS 
23rd February 2017 14:00 to 15:00 
Ivan Todorov 
HerzSchur multipliers of dynamical systems
HerzSchur multipliers of a locally compact group, introduced by
Haagerup and de Canniere in 1985, have been instrumental in operator algebra
theory in a variety of contexts, in particular in the study of approximation
properties of group operator algebras. They can be viewed as the invariant part
of the Schur multipliers  a class of maps on B(H) with another long list of
applications, e.g. in perturbation theory of linear operators. In this talk,
which is based on a joint work with A. McKee and L. Turowska, I will introduce
operatorvalued Schur and HerzSchur multipliers of arbitrary locally compact
groups. The latter give rise to natural maps on C* and von Neumann
algebra crossed products. I will present a characterisation of operatorvalued
HerzSchur multipliers as the invariant part of the operatorvalued Schur
multipliers, and will discuss various special cases which highlight the
generality of this class of maps and their potential usefulness in subsequent
research. 

OAS 
28th February 2017 14:00 to 15:00 
Evgenios Kakariadis 
Semigroup actions on operator algebras
We will present a dilation technique from
commuting endomorphisms to commuting automophisms on a larger C*algebra such
that the corresponding (minimal) CuntzNicaPimsner algebras are strong Morita
equivalent. Hence we can reduce problems on semigroup actions to problems on
group actions. Further consequences of our analysis include the association of
the ideal structure/nuclearity/exactness of the NicaPimsner algebras with
minimalityfreeness/nuclearity/exactness of the C*dynamics.


OAS 
2nd March 2017 14:00 to 15:00 
Stephen Moore 
A generalization of the TemperleyLieb algebra from restricted quantum sl2
The TemperleyLieb algebra was introduced in relation to lattice models
in statistical mechanics, before being rediscovered in the standard invariant
of subfactors. Alternatively, the TemperleyLieb algebra can be constructed as
the centralizer of the quantum group Uq(sl2). Recent work in logarithmic
conformal field theory has brought interest to a restricted version of this
quantum group. We generalize the TemperleyLieb construction to the restricted
case, describing generators and a number of relations, then describe morphisms
between modules, including a conjecture for the formula for projections onto
indecomposable modules. 

OAS 
7th March 2017 14:00 to 15:00 
Keith Hannabuss 
Tduality and the condensed matter bulkboundary correspondence
This talk will start with a brief historical review of the
classification of solids by their symmetries, and the more recent
Ktheoretic periodic table of Kitaev. It will then consider some mathematical
questions this raises, in particular about the behaviour of electrons on the
boundary of materials and in the bulk. Two rather different models will be
described, which turn out to be related by Tduality. Relevant ideas from
noncommutative geometry will be explained where needed. 

OAS 
9th March 2017 14:00 to 15:00 
Andreas Aaserud 
Approximate equivalence of measurepreserving actions
I will talk about measurepreserving actions of countable discrete
groups on probability spaces. Classically, one mainly considers two notions of
equivalence of such actions, namely conjugacy (or isomorphism) and orbit
equivalence, both of which have nice descriptions in the language of von
Neumann algebras. I will briefly discuss this classical framework before
going into some new notions of equivalence of actions. These are approximate
versions of conjugacy and orbit equivalence that were recently introduced and
investigated by Sorin Popa and myself, and which can most easily be
defined in terms of ultrapowers of von Neumann algebras. I will discuss
superrigidity within this new framework, and will also compare approximate
conjugacy to (classical) conjugacy for actions of various classes of groups.
This talk is based on joint work with Sorin Popa. 

OAS 
14th March 2017 14:00 to 15:00 
Paul Fendley 
Tutte's golden identity from a fusion category
The chromatic
polynomial \chi(Q) can be defined on any graph, such that for Q integer it
counts the number of colourings. In statistical mechanics, it is known as the
partition function of the antiferromagnetic Potts model on that graph. It has
many remarkable properties, and Tutte's golden identity is one of the more
unusual ones. For any planar triangulation, it relates \chi(\phi+2)
to the square of \chi(\phi+1), where \phi is the golden mean. Tutte's
original proof is purely combinatorial. I will give here an elementary proof
using fusion categories, which are familiar for example from topological
quantum field theory, anyonic quantum mechanics, and integrable statistical
mechanics. In this setup, the golden identity follows by simple manipulations
of a topological invariant related to the Jones polynomial. I will also mention
recent work by Agol and Krushkal on understanding what happens to the identity
for graphs on more general surfaces.


OAS 
16th March 2017 14:00 to 15:00 
Makoto Yamashita 
Weak Morita equivalence of compact quantum groups
Motivated by the 2categorical interpretation of constructs in subfactor
theory, Müger introduced the notion of weak Morita equivalence for tensor
categories. This relation roughly says that the tensor categories have the same
quantum double, or the same "representation theory". We give a
characterization of this equivalence relation for representation categories of
compact quantum groups in terms of certain commuting actions. This extends a
similar characterization of monoidal equivalence due to Schauenburg and
BichonDe RijdtVaes. Based on joint work with Sergey Neshveyev. 

OAS 
21st March 2017 14:00 to 15:00 
Yasu Kawahigashi 
A relative tensor product of rational full conformal field theories
We introduce a relative tensor product of two heterotic rational 2dimensional
conformal field theories with trivial representation theories. Such a conformal
field theory has a decomposition characterized by modular invariance, and this
gives a generalization of fusion rules of modular invariants. 

OASW02 
27th March 2017 10:00 to 11:00 
Vaughan Jones 
The semicontinuous limit of quantum spin chains
We construct certain states of a periodic quantum spin chain whose length is a power of
two and
show that they are highly uncorrelated with themselves under a rotation by one
lattice spacing.


OASW02 
27th March 2017 11:30 to 12:30 
Gus Isaac Lehrer 
Semisimple quotients of TemperleyLieb
Coauthors: Kenji Iohara
(Universite de Lyon), Ruibin Zhang
(University of Sydney)
The maximal semisimple quotients of the TemperleyLieb algebras at roots of unity are fully described by means of a presentation, and the dimensions of their simple modules are explicitly determined. Possible applications to Virasoro limits will be discussed. 

OASW02 
27th March 2017 13:30 to 14:30 
N. Christopher Phillips 
Operator algebras on L^p spaces
It has recently been discovered that there are algebras on L^pspaces
which deserve to be thought of as analogs of selfadjoint operator
algebras on Hilbert spaces (even though there is no adjoint on the
algebra of bounded operators on an L^pspace).
We have analogs of some of the most common examples of Hilbert space operator algebras, such as the AF Algebras, the irrational rotation algebras, group C*algebras and von Neumann algebras, more general crossed products, the Cuntz algebras, and a few others. We have been able to prove analogs of some of the standard theorems about these algebras. We also have some ideas towards when an operator algebra on an L^p space deserves to be considered the analog of a C*algebra or a von Neumann algebra. However, there is little general theory and there are many open questions, particularly for the analogs of von Neumann algebras. In this talk, we will try to give an overview of some of what is known and some of the interesting open questions. 

OASW02 
27th March 2017 14:30 to 15:30 
James Tener 
A geometric approach to constructing conformal nets
Conformal nets and vertex operator algebras are distinct mathematical axiomatizations of roughly the same physical idea: a twodimensional chiral conformal field theory. In this talk I will present recent work, based on ideas of André Henriques, in which local operators in conformal nets are realized as "boundary values" of vertex operators. This construction exhibits many features of conformal nets (e.g. subfactors, their Jones indices, and their fusion rules) in terms of vertex operator algebras, and I will discuss how this allows one to use Antony Wassermann's approach to calculating fusion rules in a broad class of examples.


OASW02 
27th March 2017 16:00 to 17:00 
Thomas Schick 
Geometric models for twisted Khomology
Coauthor: Paul Baum
(Penn State University)
Khomology, the homology theory dual to Ktheory, can be described in a number of quite distinct models. One of them is analytic, uses Kasparov's KKtheory, and is the home of index problems. Another one uses geometric cycles, going back to Baum and Douglas. A large part of index theory is concerned with the isomorphism between the geoemtric and the analytic model, and with Chern character transformations to (co)homology. In applications to string theory, and for certain index problems, twisted versions of Ktheory and Khomology play an essential role. We will descirbe the general context, and then focus on two new models for twisted Khomology and their applications and relations. These aere again based on geometric cycles in the spirit of Baum and Douglas. We will include in particular precise discussions of the different ways to define and work with twists (for us, classified by elements of the third integral cohomology group of the base space in question). 

OASW02 
28th March 2017 10:00 to 11:00 
Osamu Iyama 
Preprojective algebras and CalabiYau algebras
Preprojective algebras are one of the central objects in representation theory. The preprojective algebra of a quiver Q is a graded algebra whose degree zero part is the path algebra kQ of Q, and each degree i part gives a distinguished class of representations of Q, called the preprojective modules. It categorifies the Coxeter groups as reflection functors, and their structure depends on the trichotomy of quivers: Dynkin, extended Dynkin, and wild. From homological algebra point of view, the algebra kQ is hereditary (i.e. global dimension at most one), and its preprojective algebra is 2CalabiYau. In this talk, I will discuss the higher preprojective algebras P of algebras A of finite global dimension d. When d=2, then P is the Jacobi algebra of a certain quiver with potential. When A is a dhereditary algebra, a certain distinguished class of algebras of global dimension d, then its higher preprojective algebra is (d+1)CalabiYau. I will explain results and examples of higher preprojective algebras based on joint works with Herschend and Oppermann. If time permits, I will explain a joint work with Amiot and Reiten on algebraic McKay correspondence for higher preprojective algebras. 

OASW02 
28th March 2017 11:30 to 12:30 
Karin Erdmann 
Periodicity for finitedimensional selfinjective algebras
We give a survey on finitedimensional selfinjective algebras
which are periodic as bimodules, with respect to syzygies,
and hence are stably CalabiYau.
These include preprojective algebras of Dynkin types ADE and
deformations, as well a class of algebras which we call mesh algebras
of generalized Dynkin type. There is also a classification of the
selfinjective algebras of polynomial growth which are periodic.
Furthermore, we introduce weighted surface algebras, associated to
triangulations of compact surfaces, they are tame and symmetric,
and have period 4 (they are 3CalabiYau). They generalize Jacobian
algebras, and also blocks of finite groups with quaternion defect
groups.
In general, for such an algebra, all onesided simple modules are periodic. One would like to know whether the converse holds: Given a finitedimensional selfinjective algebra A for which all onesided simple modules are periodic. It is known that then some syzygy of A is isomorphic as a bimodule to some twist of A by an automorphism. It is open whether then A must be periodic. 

OASW02 
28th March 2017 13:30 to 14:30 
Alastair King 
Quivers and CFT: preprojective algebras and beyond
I will describe the intimate link between ADE preprojective algebras and Conformal Field Theories arising as SU(2) WZW models and explain some of what happens in the SU(3) case. 

OASW02 
28th March 2017 14:30 to 15:30 
Mathew Pugh 
Frobenius algebras from CFT
Coauthor: David Evans (Cardiff University) I will describe the construction of certain preprojective algebras and their generalisations arising from WZW models in Conformal Field Theory. For the case of SU(2), these algebras are the preprojective algebras of ADE type. More generally, these algebras are Frobenius algebras, and their Nakayama automorphism measures how far away the algebra is from being symmetric. I will describe how the Nakayama automorphism arises from this construction, and will describe the construction in the SO(3) case. 

OASW02 
28th March 2017 16:00 to 17:00 
Joseph Grant 
Higher preprojective algebras and higher zigzag algebras
Coauthor: Osamu Iyama
(Nagoya University)
I will give a brief introduction to preprojective algebras and higher preprojective algebras, using examples. Then I will explain some results about certain higher preprojective algebras that were obtained in joint work with Osamu Iyama, including results on periodicity and descriptions of these algebras as (higher) Jacobi algebras of quivers with potential. Finally I will explain how, in simple cases, one can define higher zigzag algebras, generalizing certain algebras studied by Huefrano and Khovanov which appear widely in geometry and representation theory. As in the classical case, one finds interesting relations between spherical twists on the derived categories of these algebras. 

OASW02 
29th March 2017 09:00 to 10:00 
Akhil Mathew 
Polynomial functors and algebraic Ktheory
The Grothendieck group K_0 of a commutative ring is wellknown to be a λring: although the exterior powers are nonadditive, they induce maps on K_0 satisfying various universal identities. The λoperations yield homomorphisms on higher Kgroups.
In joint work in progress with Glasman and Nikolaus, we give a
general framework for such operations. Namely, we show that the
Ktheory space is naturally functorial for polynomial functors, and
describe a universal property of the extended Ktheory functor. This
extends an earlier algebraic result of Dold for K_0. In this picture, the λoperations come from the strict polynomial functors of FriedlanderSuslin.


OASW02 
29th March 2017 10:00 to 11:00 
Paul Smith 
A classification of some 3CalabiYau algebras
This is a report on joint work with Izuru Mori and work of Mori and Ueyama. A graded algebra A is CalabiYau of dimension n if the homological shift A[n] is a dualizing object in the appropriate derived category. For example, polynomial rings are CalabiYau algebras. Although many examples are known, there are few if any classification results. Bocklandt proved that connected graded CalabiYau algebras are of the form TV/(dw) where TV denotes the tensor algebra on a vector space V and (dw) is the ideal generated by the cyclic partial derivatives of an element w in TV. However, it is not known exactly which w give rise to a CalabiYau algebra. We present a classification of those w for which TV/(dw) is CalabiYau in two cases: when dim(V)=3 and w is in V^{\otimes 3} and when dim(V)=2 and w is in V^{\otimes 4}. We also describe the structure of TV/(dw) in these two cases and show that (most) of them are deformation quantizations of the polynomial ring on three variables. 

OASW02 
29th March 2017 11:30 to 12:30 
Raf Bocklandt 
Local quivers and Morita theory for matrix factorizations
We will discuss how to construct a Morita theory for matrix factorizations using techniques in Mirror symmetry developed by Cho, Hong and Lau and tie this to the notion of local quivers in representation theory.


OASW02 
30th March 2017 10:00 to 11:00 
Andre Henriques 
Higher twisted Ktheory a la Dadarlat and Pennig
I will present aspects of the work of Marius Dadarlat and
Ulrich Pennig on the relation between Cuntz algebras and higher twists of
Ktheory.


OASW02 
30th March 2017 11:30 to 12:30 
Ulrich Pennig 
Equivariant higher twisted Ktheory
Twisted KTheory can be expressed in terms of section algebras of locally trivial bundles of compact operators. However, from the point of view of homotopy theory, this setup just captures a small portion of the possible twists. In joint work with Marius Dadarlat we generalised the classical theory to a C*algebraic model, which captures the higher twists of Ktheory as well and is based on strongly selfabsorbing C*algebras. In this talk I will discuss possible generalisations to the equivariant case, which is joint work with David Evans. In particular, I will first review the construction of the equivariant twist of U(n) representing the generator of its equivariant third cohomology group with respect to the conjugation action of U(n) on itself. Then I will talk about work in progress on a generalisation to (localised) higher twisted Ktheory.


OASW02 
30th March 2017 13:30 to 14:30 
Ulrich Bunke 
Homotopy theory with C*categories
In this talk I propose a presentable infinity category of
C*categories. It is modeled by a simplicial combinatorial model
category structure on the category of C*categories. This allows to set
up a theory of presheaves with values in C*categories on the orbit
category of a group together with various induction and coinduction
functors. As an application we provide a simple construction of
equivariant Ktheory spectra (first constructed by DavisLück). We
discuss further applications to equivariant coarse homology theories. Related Links 

OASW02 
30th March 2017 14:30 to 15:30 
Michael Murray 
Real bundle gerbes
Coauthors: Dr Pedram Hekmati
(University of Auckland), Professor Richard J. Szabo
(HeriotWatt University), Dr Raymond F. Vozzo
(University of Adelaide)
Bundle gerbe modules, via the notion of bundle gerbe Ktheory provide a realisation of twisted Ktheory. I will discuss the generalisation to Real bundle gerbes and Real bundle gerbe modules which realise twisted Real Ktheory in the sense of Atiyah. This is joint work with Richard Szabo, Pedram Hekmati and Raymond Vozzo and forms part of arXiv:1608.06466. Related Links


OASW02 
30th March 2017 16:00 to 17:00 
Amihay Hanany  tba  
OASW02 
31st March 2017 10:00 to 11:00 
Katrin Wendland 
Vertex Operator Algebras from CalabiYau Geometries
Vertex operator algebras occur naturally as mathematically well tractable ingredients to conformal field theories (CFTs), capturing in general only a small part of the structure of the latter. The talk will highlight a few examples for which this procedure yields a natural route from CalabiYau geometries to vertex operator algebras. Moreover, we will discuss a new technique, developed in joint work with Anne Taormina, which transforms certain CFTs into vertex operator algebras and their admissible modules, thus capturing a major part of the structure of the CFT in terms of a vertex operator algebra. 

OASW02 
31st March 2017 11:30 to 12:30 
Simon Gritschacher 
Coefficients for commutative Ktheory
Recently, the study of representation
spaces has led to the definition of a new cohomology theory, called
commutative Ktheory. This theory is a refinement of classical
topological Ktheory. It is defined using vector bundles whose
transition functions commute with each other whenever they are
simultaneously defined. I will begin the talk by discussing some
general properties of the „classifying space for commutativity in a
Lie group“ introduced by AdemGomez. Specialising to the unitary
groups, I will then show that the spectrum for commutative
complex Ktheory is precisely the kugroup ring of infinite complex
projective space. Finally, I will present some results about the real
variant of commutative Ktheory.


OASW02 
31st March 2017 13:30 to 14:30 
Danny Stevenson 
Presheaves of spaces and the Grothendieck construction in higher geometry
The notion of prestack in algebraic geometry can be formulated either in terms of categories fibered in groupoids, or else as a functor to the category of groupoids with composites only preserved up to a coherent system of natural isomorphisms. The device which lets one shift from one perspective to the other is known as the `Grothendieck construction' in category theory. A presheaf in higher geometry is a functor to the ∞category of ∞groupoids; in this context keeping track of all the coherent natural isomorphisms between composites becomes particularly acute. Fortunately there is an analog of the Grothendieck construction in this context, due to Lurie, which lets one `straighten out' a presheaf into a certain kind of fibration. In this talk we will give a new perspective on this straightening procedure which allows for a more conceptual proof of Lurie's straightening theorem. 

OASW02 
31st March 2017 14:30 to 15:30 
YangHui He 
CalabiYau volumes and Reflexive Polytopes
We study various geometrical quantities for CalabiYau varieties
realized as cones over Gorenstein
Fano varieties in various dimensions, obtained as toric varieties from
reflexive polytopes.
One chief inspiration comes from the equivalence of amaximization and volumeminimization in for CalabiYau threefolds, coming from AdS5/CFT4 correspondence in physics. We arrive at explicit combinatorial formulae for many topological quantities and conjecture new bounds to the SasakiEinstein volume function with respect to these quantities. Based on joint work with RakKyeong Seong and ShiingTung Yau. 

OAS 
6th April 2017 13:00 to 14:00 
Valeriano Aiello 
The oriented Thompson group, oriented links, and polynomial link invariants
Recently, Vaughan Jones discovered an unexpected connection between the
Thompson groups and knots. Among other things, he showed that any
oriented link can be obtained as the "closure" of elements of the
oriented Thompson group $\vec{F}$. By using this procedure we show that certain
specializations of some link invariants, notably the Homfly polynomial, are
functions of positive type on $\vec{F}$ (up to a renormalization). As for
other specializations, we also show that the corresponding functions are not
even bounded (in particular, they are not of positive type). This talk is based
on a joint work with Roberto Conti (Sapienza Università di Roma) and Vaughan
Jones (Vanderbilt University). 

OAS 
11th April 2017 14:00 to 15:00 
Kenny De Commer 
Ifactorial quantum torsors and Heisenberg algebras of quantized enveloping type
A Ifactorial quantum torsor consists of an integrable, free and ergodic action
of a locally compact quantum group on a type Ifactor. We show how such actions
admit a nice duality theory. As an example, we consider a deformed Heisenberg
algebra associated to a quantum Borel algebra of a semisimple complex Lie
algebra g. We show that, endowed with a *structure swapping the two quantum
Borel algebras inside, it allows a completion into a Ifactorial quantum torsor
for (an amplification of) the von Neumann algebraic completion of the compact
form of the quantized enveloping algebra of g. 

OAS 
18th April 2017 14:00 to 15:00 
Yuki Arano 
Representation theory of Drinfeld doubles (Part 1)
We study the representation theory of Drinfeld doubles of qdeformations
via the analogy with that of complex semisimple Lie groups. As applications, we
prove central property (T) for general higher rank qdeformations and a
HoweMoore type theorem for qdeformations. We also review how these properties
can be interpreted in terms of tensor categories and subfactors. 

OAS 
20th April 2017 14:00 to 15:00 
Andrew McKee 
HerzSchur multipliers and approximation properties
HerzSchur multipliers of a discrete group have proved useful in the
study of $C^*$algebras, as they can be used to link properties of the group to
approximation properties of the reduced group $C^*$algebra. The development of
these ideas has shed light on some $C^*$algebra properties, and motivated the
introduction and study of others. I will introduce HerzSchur multipliers, and discuss some of their applications, before describing a generalisation of these functions to multipliers of a $C^*$dynamical system. In the final part of the talk I will show how the generalised HerzSchur multipliers can be used to study approximation properties of the reduced crossed product formed by a group acting on a $C^*$algebra, paralleling the applications of HerzSchur multipliers; these new tools allow us to study approximation properties of the reduced crossed product without requiring the group to be amenable. 

OAS 
25th April 2017 14:00 to 15:00 
Yuki Arano 
Representation theory of Drinfeld doubles (Part 2)
We study the representation theory of Drinfeld doubles of qdeformations
via the analogy with that of complex semisimple Lie groups. As applications, we
prove central property (T) for general higher rank qdeformations and a
HoweMoore type theorem for qdeformations. We also review how these properties
can be interpreted in terms of tensor categories and subfactors. 

OAS 
27th April 2017 14:00 to 15:00 
Ingo Runkel 
Traces in nonsemisimple categories
Quite generally, a trace on a klinear category is a
family of functions from the endomorphisms of objects to the underlying field
k, subject to cyclicity and possibly other constraints. In some interesting
cases these functions may only exist for a subset of all objects. One situation
where this may happen are nonsemisimple braided finite tensor categories,
which have applications in link invariants and in twodimensional conformal
field theory. In this talk I will present some results and conjectures related
to such categories. 

OAS 
2nd May 2017 14:00 to 15:00 
Yuki Arano 
Representation theory of Drinfeld doubles (Part 3)
We study the representation theory of Drinfeld doubles of qdeformations
via the analogy with that of complex semisimple Lie groups. As applications, we
prove central property (T) for general higher rank qdeformations and a
HoweMoore type theorem for qdeformations. We also review how these properties
can be interpreted in terms of tensor categories and subfactors. 

OAS 
4th May 2017 14:00 to 15:00 
Roland Vergnioux 
Free entropy dimension and the orthogonal free quantum groups
Orthogonal free quantum groups have been extensively studied in the past
two decades from the operator algebraic point of view, and were shown to share
many analytical properties with the ordinary free groups. In a recent preprint
with Michael Brannan, we prove that the associated von Neumann algebras are
strongly 1bounded in the sense of Jung. In particular, they are not isomorphic
to free group factors. This result is obtained by establishing a spectral
regularity result for the edge reversing operator on the associated quantum
Cayley tree, and combining this result with a recent free entropy
dimension rank theorem of Jung and Shlyakhtenko. 

OAS 
9th May 2017 14:00 to 15:00 
Yuki Arano 
Representation theory of Drinfeld doubles (Part 4)
We study the representation theory of Drinfeld doubles of qdeformations
via the analogy with that of complex semisimple Lie groups. As applications, we
prove central property (T) for general higher rank qdeformations and a
HoweMoore type theorem for qdeformations. We also review how these properties
can be interpreted in terms of tensor categories and subfactors. 

OAS 
16th May 2017 12:45 to 13:45 
Dorothea Bahns 
Rieffel deformation, tempered distributions and the Gabor wavefront set
I will give gentle introduction to microlocal analysis and how to use it to define R^n Rieffel deformed products of tempered distributions. Applications of this include quantum field theory on the noncommutative Moyal space or certain warped products. It also answers the question how to extend the Weyl calculus to tempered distributions. This is joint work with René Schulz.


OAS 
16th May 2017 14:00 to 15:00 
Hans Wenzl 
Subfactors related to certain symmetric spaces
One of the first examples of subfactors came
from groups and subgroups. In this talk we construct subfactors which can
be considered analogs of the embeddings of O(N) into U(N) in the setting of
fusion categories. These are finite depth subfactors whose indices will
go to infinity in the classical limit. Its principal graph will give the
inductionrestriction graph of these groups in the limit.


OAS 
18th May 2017 14:00 to 15:00 
David Kyed 
L^2Betti numbers of universal quantum groups
I will report on joint works with Julien Bichon, Sven Raum, Matthias
Valvekens and Stefaan Vaes, revolving around the computation of L^2Betti
numbers for universal quantum groups. Among our main results is the fact
that the first L^2Betti number of the duals of the free unitary quantum groups
equals 1, and that all other L^2Betti numbers vanish. All objects
mentioned in the abstract will be defined, more or less rigorously, during the
talk. 

OAS 
23rd May 2017 14:00 to 15:00 
YingFen Lin 
Nilpotent Lie groups: Fourier inversion and prime ideals
In this talk, I will give a version of the
Fourier inversion theorem for connected, simply connected nilpotent Lie groups
G = exp(g) by showing that there is a continuous retract from the space of
adapted smooth kernel functions defined on a submanifold of g^* into the
Schwartz functions defined on G. As an application, I will give a
characterisation of a class of invariant prime ideals of L^1(G).


OAS 
25th May 2017 14:00 to 15:00 
Jonathan Rosenberg 
H^3 and twisted Ktheory for compact Lie groups
The WZW model in physics naturally leads to a
study of twisted Ktheory for compact Lie groups, which has been studied by
MooreMaldacenaSeiberg, Hopkins, Braun, and Douglas. We reexamine a few
aspects of this subject. For example, what is the map on H^3 induced by a
covering of compact simple Lie groups? The result is complicated and
quite surprising. Also, what can we learn about twisted Ktheory from the
connection between Langlands duality and Tduality, studied by DaenzerVan Erp
and BunkeNikolaus? Again, the result is rather surprising. This is
joint work with Mathai Varghese.


OAS 
2nd June 2017 16:00 to 17:00 
Marius Dadarlat 
Introduction to continuous fields of C*algebras and their topological invariants (Part 1)
Continuous fields play the
role of bundles of C*algebras (in the sense of topology). The bundle structure
that underlines a continuous fields is typically not locally trivial. We will start by introducing various classes of examples. Thereafter, we will discuss obstructions to local triviality and give an introduction to topological invariants such as parametrized Ktheory. Finally, we will present a generalized DixmierDouady theory obtained in joint work with Ulrich Pennig. 

OAS 
6th June 2017 12:45 to 13:45 
Joachim Zacharias 
Bivariant and Dynamical Versions of the Cuntz Semigroup
The Cuntz Semigroup is an
invariant for C*algebras combining Ktheoretical and tracial information. It
can be regarded as a C*analogue of the MurrayvonNeumann semigroup of
projections of a von Neumann algebra. The Cuntz semigroup plays an increasingly
important role in the classification of simple C*algebras. We propose a
bivariant version of the Cuntz Semigroup based on equivalence classes of order
zero maps between a given pair of C*algebras. The resulting bivariant
theory behaves similarly to Kasparov's KKtheory: it contains the ordinary
Cuntz Semigroup as a special case just as KKtheory contains Ktheory
and admits a composition product. It can be described in different
pictures similarly to the classical Cuntz Semigroup and behaves well with
respect to various stabilisations. Many properties of the ordinary Cuntz
Semigroup have bivariant counterparts. Whilst in general hard to determine, the
bivariant Cuntz Semigroup can be computed in some special cases. Moreover, it
can be used to classify stably finite algebras in analogy to the
KirchbergPhillips classification of simple purely infinite algebras via
KKtheory. We also indicate how an equivariant version of the bivariant Cuntz
Semigroup can be defined, at least for compact groups. If time permits, we
discuss recent work in progress on a version of the Cuntz Semigroup for
dynamical systems, more precisely, groups acting on compact spaces, with
potential applications to classifiability of crossed products. (Joint work with
Joan Bosa, Gabriele Tornetta.) 

OAS 
6th June 2017 14:00 to 15:00 
Marius Dadarlat 
Introduction to continuous fields of C*algebras and their topological invariants (Part 2)
Continuous fields play the role of bundles of C*algebras (in the
sense of topology). The bundle structure that underlines a continuous
fields is typically not locally trivial. We will start by introducing various classes of examples. Thereafter, we will discuss obstructions to local triviality and give an introduction to topological invariants such as parametrized Ktheory. Finally, we will present a generalized DixmierDouady theory obtained in joint work with Ulrich Pennig. 

OAS 
8th June 2017 12:45 to 13:45 
Emmanuel Germain 
Pimsner legacy
We will discuss two major contributions of Mihai Pimsner about
computations of KKtheory of C*algebras from the 80's and 90's and show how
their scope can be greatly expanded using techniques that are somehow more
combinatorial than the classical 'analytical' interpretation. 

OAS 
8th June 2017 14:00 to 15:00 
Marius Dadarlat 
Introduction to continuous fields of C*algebras and their topological invariants (Part 3)
Continuous fields play the
role of bundles of C*algebras (in the sense of topology). The bundle structure
that underlines a continuous fields is typically not locally trivial. We will start by introducing various classes of examples. Thereafter, we will discuss obstructions to local triviality and give an introduction to topological invariants such as parametrized Ktheory. Finally, we will present a generalized DixmierDouady theory obtained in joint work with Ulrich Pennig. 

OASW03 
12th June 2017 10:00 to 11:00 
Vaughan Jones 
Phase transitions in the semicontinuous limit of a quantum spin chain
A quest for the
construction of a conformal field theory directly from a subfactor has taken an
unexpected turn involving a "semicontinuous limit” Hilbert space, with
Thompson group symmetry, that might be as relevant to critical quantum spin
chains as CFT itself. Models give spin chains with various phases governed by
the value of a spectral parameter, and a holomorphic dynamical system. The
phases are the Fatou connected components of the dynamical system and the phase
transistions occur when the spectral parameter crosses the Julia set from one
Fatou component to another.


OASW03 
12th June 2017 11:30 to 12:30 
Arthur Jaffe 
On Picture Language
We introduce some recent work on pictures and the development of the quon language (joint work with Zhengwei Liu and Alex Wozniakowski). We describe a pictorial journey from planar algebras and parafermions, through a problem in quantum information.


OASW03 
12th June 2017 13:30 to 14:30 
Yasu Kawahigashi 
The relative Drinfeld commutant and alphainduction
We study relative Drinfeld commutants of a fusion category in another
fusion category in terms of halfbraidings. We identify halfbraidings
with minimal central projections of the relative tube algebra and
certain sectors related to the LongoRehren subfactors. We apply this general
machinery to various fusion categories arising from alphainduction applied to a modular tensor category and
compute the relative Drinfeld commutants explicitly.


OASW03 
12th June 2017 14:30 to 15:30 
Roberto Longo  Discussion about the Landauer principle (and bound)  
OASW03 
12th June 2017 16:00 to 17:00 
Stefaan Vaes 
Rothschild Lecture: Classification of von Neumann algebras
The theme of this talk is the dichotomy between amenability and nonamenability. Because the group of motions of the threedimensional Euclidean space is nonamenable (as a group with the discrete topology), we have the BanachTarski paradox. In dimension two, the group of motions is amenable and there is therefore no paradoxical decomposition of the disk. This dichotomy is most apparent in the theory of von Neumann algebras: the amenable ones are completely classified by the work of Connes and Haagerup, while the nonamenable ones give rise to amazing rigidity theorems, especially within Sorin Popa's deformation/rigidity theory. I will illustrate the gap between amenability and nonamenability for von Neumann algebras associated with countable groups, with locally compact groups, and with group actions on probability spaces. 

OASW03 
13th June 2017 09:00 to 10:00 
Dietmar Bisch  Subfactors with infinite representation theory  
OASW03 
13th June 2017 10:00 to 11:00 
Zhengwei Liu 
Synergy on quon language
We will talk about the discovery of the quon language, which was inspired by ideas in different areas: subfactors, quantum information, CFT, TQFT. New proofs and results were carried out by synergy on the quon language. The Fourier analysis on quons turns out to be powerful to study modular tensor categories.


OASW03 
13th June 2017 11:30 to 12:30 
Hubert Saleur 
Associative algebras and conformal field theories
I will review in this talk the relationships physicists observe/conjecture between the associative algebras (such as TemperleyLieb) that appear in lattice models, and the conformal field theories (CFT) that describe their continuum limits. I will then discuss in more detail a possible way to perform "fusion" for affine TemperleyLieb modules, and what this may have to do with Operator Product Expansion (OPE) in CFT. 

OASW03 
13th June 2017 13:30 to 14:30 
Paul Fendley 
Baxterising using conserved currents
Many integrable critical classical statistical mechanical models and the corresponding quantum spin chains possess an unusual sort of conserved current. Such currents have been constructed by utilising quantumgroup algebras, fermionic and parafermionic operators, and ideas from ``discrete holomorphicity''. I define them generally and naturally using a braided tensor category, a structure familiar from the study of knot invariants and from conformal field theory. Requiring the existence of the currents provides a simple way of ``Baxterising'', i.e. building a solution of the YangBaxter equation out of topological data. This approach allows many new examples of conserved currents to be found, for example in height models. Although integrable models found by this construction are critical, I find one noncritical generalisation: requiring a ``shift'' operator in the chiral clock chain yields precisely the Hamiltonian of the integrable chiral Potts chain. 

OASW03 
13th June 2017 14:30 to 15:30 
Gandalf Lechner 
YangBaxter representations of the infinite symmetric group
The YangBaxter equation (YBE) lies at the heart of many subjects, including quantum statistical mechanics, QFT, knot theory, braid groups, and subfactors. In this talk, I will consider involutive solutions of the YBE ("Rmatrices"). Any such Rmatrix defines a representation and an extremal character of the infinite symmetric group as well as a corresponding tower of subfactors. Using these structures, I will describe how to find all Rmatrices up to a natural notion of equivalence (given by the character and the dimension), how to completely parameterize the set of solutions, and how to decide efficiently whether two given Rmatrices are equivalent. Joint work with U. Pennig and S. Wood. 

OASW03 
13th June 2017 16:00 to 17:00 
Kasia Rejner 
The Quantum SineGordon model in perturbative AQFT
Coauthor: Dorothea Bahns (University of Goettingen) In this talk I will present recent results on the convergence of the formal Smatrix and interacting currents in the SineGordon model in 2 dimensions, obtained directly in Minkowski signature, using a class of Hadamard states. In our approach one starts with a perturbation series obtained from the formalism of perturbative AQFT and then one can prove the convergence of the series by some simple estimates. Our result opens the posibility to use pAQFT methods to study integrable models in 2 dimensions and to construct local observables in such models. Related Links


OASW03 
14th June 2017 09:00 to 10:00 
Constantin Teleman 
KramerWannier and electromagnetic duality in field theory
A classical duality (KramerWannier) relates the low and high temperature of the 2dimensional Ising model. It has been generalized to other dimensions and groups other than Z/2 and distilled into Poincare duality combined with the Abelian Fourier transform. In this talk, I describe a vast generalization in the language of topological field theories, which includes nonAbelian examples. Via the notion of boundary field theory, thus is related to a duality of TQFTs, specifically electromagnetic duality in 3 dimensions. There arises a natural speculation about invertibility of gapped phases in a large class of lattice models. This is joint work (in progress) with Dan Freed.


OASW03 
14th June 2017 10:00 to 11:00 
Pedram Hekmati 
An application of Tduality to Ktheory
Coauthor: David Baraglia (The University of Adelaide) Tduality is a discrete symmetry that was discovered by physicists in the context of string theory, but has now matured into a precise mathematical statement. In this talk I will give a brief overview of topological Tduality and explain how it can be used to give a new, surprisingly simple proof of Hodgkin’s famous theorem on the Ktheory of compact simply connected Lie groups. 

OASW03 
14th June 2017 11:30 to 12:30 
Giovanni Landi 
Line bundles over noncommutative spaces
We give a Pimsner algebra construction of noncommutative lens spaces as `direct sums of line bundles' and exhibit them as `total spaces' of certain principal bundles over noncommutative weighted projective spaces. For each quantum lens space one gets an analogue of the classical Gysin sequence relating the KK theory of the total space algebra to that of the base space one. This can be used to give explicit geometric representatives of the Ktheory classes of the lens spaces.


OASW03 
15th June 2017 09:00 to 10:00 
Antony Wassermann  Conformal Field Theory, Operator algebras and symmetric Fuchsian equations  
OASW03 
15th June 2017 10:00 to 11:00 
Robin Hillier 
Loop groups and noncommutative geometry
I describe a way of expressing loop groups and their representation theories (the Verlinde fusion ring) in terms of spectral triples and KKtheory. The ideas come from operator algebraic conformal field theory and extend to many other conformal field theoretical models. Coauthor: Sebastiano Carpi. 

OASW03 
15th June 2017 11:30 to 12:30 
Ralf Meyer 
Induced C*hulls for *algebras
Let A be a *algebra that is graded by a group G with fibres A_g for g in G. Assume that we have found a C*algebra B_e whose “representations” are “equivalent” to the “integrable” “representations” of the unit fibre A_e. Call a “representation” of A “integrable”, if its restriction to A_e is “integrable”. Under some assumptions, the “integrable” “representations” of A are “equivalent ” to the “representations” of a certain C*algebra B constructed from B_e and the graded *algebra A. The C*algebra B is the section C*algebra of a Fell bundle over G. The words in quotation marks have to be interpreted carefully to make this true. In particular, representations must be understood to take place on Hilbert modules, not just Hilbert spaces, and the equivalence is required natural with respect to induction of representations and isometric intertwiners. Under some commutativity assumptions, the main result of my lecture has been proved by Savchuk and Schmüdgen, who also give several examples. A sample of the result concerns Weyl algebras and twisted Weyl algebras in countably many generators. These come with a canonical grading by the free Abelian group on countably many generators. 

OASW03 
15th June 2017 13:30 to 14:30 
Christian Voigt 
The string group and vertex algebras
I will describe a categorification of complex Clifford algebras arising from certain categories of twisted modules over fermionic vertex superalgebras. Along the way I'll discuss some background from the theory of unitary vertex algebras, and how the String 2group fits into the picture.


OASW03 
15th June 2017 14:30 to 15:30 
Andre Henriques 
Bicommutant categories
Bicommutant categories are higher categorical analogs of von Neumann algebras. There exist currently two sources of examples of bicommutant categories: unitary fusion categories, and completely rational unitary conformal field theories. I will give a general introduction on what and why bicommutant categories are. Then I will talk about a recent result with Dave Penneys: Morita equivalent unitary fusion categories have isomorphic associated bicommutant categories. 

OASW03 
15th June 2017 16:00 to 17:00 
Lilit Martirosyan 
Affine centralizer algebras
I will describe the representations of (affine) centralizer algebras for quantum groups in terms of paths. I will talk about generators for these algebras. As an example, we will consider the Lie algebra $G_2$ and its centralizer algebras. 

OASW03 
16th June 2017 09:00 to 10:00 
Feng Xu  On questions around reconstruction program  
OASW03 
16th June 2017 10:00 to 11:00 
Ching Hung Lam 
On the Classification of holomorphic vertex operator algebras of central charge 24
In 1993, Schellekens obtained a list of possible Lie algebra structures for the weight one subspaces of holomorphic vertex operator algebras (VOA) of central charge 24. It was also conjectured that the VOA structure of a holomorphic VOA of central charge 24 is uniquely determined by the Lie algebra structure of its weight one space. Recently, all 71 cases in Schellekens' list have been constructed. In this talk, we will discuss the recent progress on the classification of holomorphic vertex operator algebras of central charge 24. In particular, we will discuss the construction of holomorphic VOAs using various types of orbifold constructions. A technique, which we call ``Reverse orbifold construction", will also be discussed. This technique may be used to prove the uniqueness of holomorphic VOAs of central charge 24 if the weight one subspace is not zero. 

OASW03 
16th June 2017 11:30 to 12:30 
Simon Wood 
What to expect from logarithmic conformal field theory
Logarithmic conformal field theory is a generalisation of ordinary conformal field theory that allows for logarithmic singularities in correlation functions. This implies the existence of reducible yet indecomposable modules on which the action of the Virasoro L_0 operator is not diagonalisable. In this talk I will recall some of what is known about rational conformal field theory and contrast it with what has been achieved so far in logarithmic conformal field theory. 

OASW03 
16th June 2017 13:30 to 14:30 
Sebastiano Carpi 
Conformal nets, VOAs and their representations
We discuss some recent results on the connection between conformal nets, VOAs and their representation theories.


OASW03 
16th June 2017 14:30 to 15:30 
Terry Gannon 
The truth about finite group orbifolds
Chiral CFTs (VOAs or conformal nets) are interesting for their representation theory. Orbifolds are a standard method for constructing new chiral CFTs from old ones. Start with a chiral theory with trivial representation theory, and orbifold it by a finite group; the result (called a holomorphic orbifold) has the representation theory given by the twisted Drinfeld double of that finite group, where the twist is a 3cocycle. In practise it is hard to identify that twist. I'll begin my talk by giving some examples of orbifolds. I'll identify a wellknown class of holomorphic orbifolds where we now know the twist. I'll relate holomorphic orbifolds to KKtheory as well as the PhD thesis of a certain Vaughan Jones. Then I'll explain how any choice of finite group and 3cocycle is realized by a chiral CFT. This is joint work with David Evans. 

OAS 
20th June 2017 13:30 to 14:30 
Sven Raum 
Groups acting on trees: representation theory and operator algebras
This talk summarises different aspects of my work on totally
disconnected groups, their representation theory and their operator
algebras. Our guiding examples are nondiscrete groups acting on
trees. I will address simplicity, amenability and classification of
operator algebras associated with groups acting on trees as well as
representation theoretic aspects such as the admissibility conjecture. 

OAS 
20th June 2017 16:00 to 17:00 
Masaki Izumi 
Group actions on C*algebras and obstruction theory
This talk gives an account of the roles in group
actions on C*algebras played by the classical obstruction theory for fiber
bundles. More specifically, I discuss the following deciding problems: (1) whether a given 2cocycle action is equivalent to an ordinary action or not, (2) whether a given 1cocycle of an action is an (asymptotic) coboundary or not, (3) whether two given actions are cocycle conjugate or not. The idea works well for polyZ groups on Kirchberg algebras. This is joint work with Hiroki Matui. 