Primer on subfactors and applications
Wednesday 11th January 2017 to Friday 20th January 2017
12:30 to 13:30  Lunch at Wolfson Court  
13:00 to 13:30  Registration  
13:30 to 15:00 
David Penneys (University of California, Los Angeles) 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.

INI 2  
15:00 to 16:30 
Yasu Kawahigashi (University of Tokyo) 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.

INI 2 
12:30 to 13:30  Lunch at Wolfson Court  
13:30 to 15:00 
David Penneys (University of California, Los Angeles) 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.

INI 2  
15:00 to 16:30 
Yasu Kawahigashi (University of Tokyo) 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.

INI 2 
12:30 to 13:30  Lunch at Wolfson Court  
13:30 to 15:00 
David Penneys (University of California, Los Angeles) 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.

INI 2  
15:00 to 16:30 
Yasu Kawahigashi (University of Tokyo) 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.

INI 2 
12:30 to 13:30  Lunch at Wolfson Court  
13:30 to 15:00 
David Penneys (University of California, Los Angeles) 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.

INI 2  
15:00 to 16:30 
Yasu Kawahigashi (University of Tokyo) 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.

INI 2 
12:30 to 13:30  Lunch at Wolfson Court  
13:30 to 15:00 
Roberto Longo (Università degli Studi di Roma Tor Vergata) Operator Algebras and Conformal Field Theory 
INI 2 
15:00 to 16:30 
Stefaan Vaes (KU Leuven) 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.

INI 2 
09:00 to 10:30 
Roberto Longo (Università degli Studi di Roma Tor Vergata) Operator Algebras and Conformal Field Theory 
INI 2  
10:30 to 12:00 
Stefaan Vaes (KU Leuven) 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.

INI 2  
12:30 to 13:30  Lunch at Wolfson Court 
12:30 to 13:30  Lunch at Wolfson Court  
13:30 to 15:00 
Roberto Longo (Università degli Studi di Roma Tor Vergata) Operator Algebras and Conformal Field Theory 
INI 2  
15:00 to 16:30 
Stefaan Vaes (KU Leuven) 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.

INI 2 
09:00 to 10:30 
Roberto Longo (Università degli Studi di Roma Tor Vergata) Operator Algebras and Conformal Field Theory 
INI 2 
10:30 to 12:00 
Stefaan Vaes (KU Leuven) 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.

INI 2 
12:30 to 13:30  Lunch at Wolfson Court 