| Abstract: |
The extended Haagerup subfactor is the last unknown item on Haagerup's 1993 list of possible small-index subfactors. In recent work with Stephen Bigelow, Scott Morrison and Noah Snyder we construct this subfactor by constructing its associated planar algebra. This finishes the classification of subfactors with index up to $3+\sqrt{2}$. I will start this talk by introducing planar algebras, an extremely useful invariant of subfactors, and then discuss the classification of small-index subfactors/planar algebras. This classification points to the existence of `exotic' planar algebras, which are planar algebras that aren't part of known algebraic families (such as those coming from groups or quantum groups), and I will discuss techniques for constructing these objects.
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