Noah Snyder

Skein theory for the D_2pi planar algebras

Abstract We give a combinatorial description of the “ D 2 n planar algebra”, by generators and relations. We explain how the generator interacts with the Temperley–Lieb braiding. This shows the previously known braiding on the even part extends to a ‘braiding up to sign’ on the entire planar algebra. We give a direct proof that our relations are consistent (using this ‘braiding up to sign’), give a complete description of the associated tensor category and principal graph, and show that the planar algebra is positive definite. These facts allow us to identify our combinatorial construction with the standard invariant of the subfactor D 2 n .

The classification of subfactors of index at most 5

The first author was supported by the NSF under Grant No. DMS-0301173 The second author was supported by the Australian Research Council under the Discovery Early Career Researcher Award DE120100232, and Discovery Project DP140100732 The third author was supported by a NSF Postdoctoral Fellowship at Columbia University. All authors were supported by DARPA grants HR0011-11-1-0001 and HR0011-12-1-0009.

Subfactors of index less than 5, Part 1: The principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than A∞ subfactors, of index between 4 and 5. Previously this classification was known up to index

Quantum Subgroups of the Haagerup Fusion Categories

{3+\sqrt{3}}

Non-cyclotomic fusion categories

. In the first paper we give an analogue of Haagerup’s initial classification of subfactors of index less than

Knot polynomial identities and quantum group coincidences

{3+\sqrt{3}}