# Timetable (OASW04)

## 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 2-category, 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 Tomita-Takesaki theory, type III subfactors, tensor categories, braiding, quantum doubles, alpha-induction 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 2-category, 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 Tomita-Takesaki theory, type III subfactors, tensor categories, braiding, quantum doubles, alpha-induction 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 2-category, 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 Tomita-Takesaki theory, type III subfactors, tensor categories, braiding, quantum doubles, alpha-induction 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 2-category, 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 Tomita-Takesaki theory, type III subfactors, tensor categories, braiding, quantum doubles, alpha-induction 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^2-Betti numbers for subfactors The standard invariant of a subfactor can be viewed in different ways as a discrete group like'' mathematical structure - a lambda-lattice 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^2-Betti numbers for subfactors The standard invariant of a subfactor can be viewed in different ways as a discrete group like'' mathematical structure - a lambda-lattice 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^2-Betti numbers for subfactors The standard invariant of a subfactor can be viewed in different ways as a discrete group like'' mathematical structure - a lambda-lattice 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^2-Betti numbers for subfactors The standard invariant of a subfactor can be viewed in different ways as a discrete group like'' mathematical structure - a lambda-lattice 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