**DISTINGUISHED LECTURE SERIES**

**Supported by the
Ascher Mallah Grant**

**Professor Vaughan F.R. Jones
University of California, Berkeley
Fields Medalist**

will deliver a series of lectures

to be held in

**Room 232
Amado Mathematics Building
Technion - Israel Institute of Technology
Haifa, Israel**

Lecture I: Monday, 18 March, 2002 — 15:30

**SUBFACTORS**

In this talk I will give an historic account of the early development of subfactors including definitions of the basic ingredients — Hilbert space and operators thereon. Much will be made of an analogy with Galois theory. Von Neumann's continuous dimension will give the analogue of the degree of an extension for an extension of von Neumann algebras.

Lecture II: Wednesday, 20 March 2002—15:30

**LOOP GROUPS AND SUBFACTORS**

This talk will present the search for subfactors occurring naturally in a
context quite distinct from the original one. This search was eventually completed by
Antony Wassermann. It will involve detours into quantum field theory, low dimensional
topology, statistical mechanics, affine Lie algebras and representation theory of compact
groups.

Lecture III: Thursday, 21 March 2002 — 15:30

**PLANAR
ALGEBRAS**

This talk will present the definition and some basic examples of planar algebras, a structure that grew out of and axiomatizes subfactors (by a result of Popa). The talk will be completely elementary and independent of the second talk. A planar algebra is a structure with many "multiplications" indexed by planar diagrams.