Speaker: Marta Asaeda
Title: Non-existense of finite depth subfactors with certain small indices
Abstract: (With S.Yasuda.) In 1991 Haagerup gave the list of graphs as
candidates of principal graphs of subfactors with indices within
(4; 3 +\sqrt{3}). We prove that one of the parametrized series of the
graphs are not realized as principal graphs except for the first two,
using algebraic number theory.
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Speaker: Richard Burstein
Title: Subfactors and Hadamard Matrices
Abstract: A II_1 subfactor may be obtained from a symmetric commuting square via
iteration of the basic construction. One class of commuting squares is
obtained from generalized Hadamard matrices. The standard invariant of
such a Hadamard subfactor may be computed to any level in finite time,
but their general classication remains intractable.
I will discuss how a certain twisted tensor product of Hadamard
matrices produces a subfactor of the form M^G \in (M \rtimes H).
G and H generate a group K in Out(M), with an associated 3-cocycle
\lambda. The principal graph may then be computed from K using the
methods of Bisch and Haagerup. By considering \lambda as well, we may
sometimes obtain a classification up to subfactor isomorphism.
I will give several examples, including a full classification of
Hadamard subfactors of index 4.
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Speaker: Paramita Das
Title: The planar algebra of Bisch-Haagerup subfactors I
Abstract: We describe the planar algebra, or equivalently, the standard
invariant, of the subfactor $P^H \subset P \rtimes K$ arising from
outer actions of two finite groups $H$ and $K$ on a $II_1$-factor $P$
assuming that the group generated by $H$ and $K$ in $Aut(P)$
intersects trivially with $Inn(P)$. The planar algebra has an
interesting similarity with IRF models in Statistical Mechanics. This
is a joint work with Dietmar Bisch and Shamindra Ghosh.
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Speaker: Shamindra Ghosh
Title: The planar algebra of Bisch-Haagerup subfactors II
Abstract: We describe the planar algebra associated to the subfactor
$P^H \subset P \rtimes K$ for outer actions of any two finite groups
$H$ and $K$ on a $II_1$-factor $P$ with no extra assumption. These
subfactors were introduced by Bisch and Haagerup some 10 years ago and
play an important role in the theory since they provide a very simple
mechanism to construct irreducible subfactors whose standard invariant
has infinite depth. The planar algebra heavily depends on the cocycle
arising as an obstruction to lifting the subgroup $G$ in $Out(P)$
generated by $H$ and $K$. This is joint work with Dietmar Bisch and
Paramita Das.
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Speaker: Pinhas Grossman
Title: Construction of a subfactor with index $(7+\sqrt{13})/2 $ (after
Masaki Izumi)
Abstract: A subfactor with index $(7+\sqrt{13})/2 $ was constructed by Izumi by
showing the existence of a Q-system associated to a certain bimodule
appearing in the fusion algebra of the Haagerup subfactor.
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Speaker: Vaughan Jones
Title: Pairs of finite index subfactors, systems of bimodules and II_1
factors coming from graded algebras
Abstract: TBA
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Speaker: Yasuyuki Kawahigashi
Title: Superconformal field theory, super moonshine and operator algebras
Abstract: We study superconformal field theory through nets of von Neumann
algebras realized with representations of the super Virasoro algebras.
In particular, we make an operator algebraic study of Duncan's super
moonshine for Conway's sporadic finite simple group Co_1.
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Speaker: Scott Morrison
Title: A not-quite-braiding for the D_2n planar algebras and some knot
invariants
Abstract: Joint work with Emily Peters and Noah Snyder. I'll describe in detail
the planar algebra associated to the subfactor with principal graph
D_{2n}. We'll see that there isn't quite a braiding on the tensor
category of bimodules, but instead something that's almost as good.
I'll explain how to use this to define some knot and link invariants,
and prove some coincidences for small n. As a result, we get some nice
identities between certain evaluations of coloured Jones polynomials.
These look like they have nothing to do with D_2n (or indeed
subfactors), but I don't know of any direct explanation for them!
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Speaker: Emily Peters
Title: Constructing the Haagerup subfactor with planar algebras
Abstract: Planar algebras capture the rich structure of the tower of relative
commutants, the main invariant of a subfactor. The reverse also
works: Subfactors can be constructed from (nice) planar algebras. I
will give a generators and relations construction of the Haagerup
planar algebra (the planar algebra which gives the Haagerup
subfactor), and describe how it was found -- where to look for such a
planar algebra, how to recognize it, and how to be sure it's the right
planar algebra.
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Speaker: Jesse Peterson
Title: von Neumann subalgebras closed under $(\Gamma)$-extensions
Abstract: Given a finite von Neumann algebra $N$, we will say that a diffuse
subalgebra $B$ is closed under ($\Gamma$)-extensions in $N$ if
whenever $P \subset N$ is a subalgebra with $P \cap B$ diffuse and
$P \cap N^\omega$ diffuse for some free ultrafilter $\omega$ then we
have $P \subset B$. We show that if $\delta$ is a densely defined
closable derivation into the Hilbert-Schmidt operators which is of the
form $\delta(x) = [D; x]$, for some $D \in B(L^2N)$ then
$\ker(\delta)$ is closed under ($\Gamma$)-extensions in $N$. In
particular if $\ker(\delta)$ is injective then it is maximal injective
and we obtain generalizations of results of Popa and Ge on maximal
injective subalgebras. Also by applying this result to derivations
coming from group cocycles we show that if $G$ is a countable discrete
group with a proper $\ell2$-cocycle and if $H < G$ is an infinite
maximal amenable subgroup then $LH$ is maximal injective in $LG$.
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Speaker: Noah Snyder
Title: Unoriented or Disoriented?
Abstract: The Temperley-Lieb algebra comes in many different flavors:
shaded/unshaded, oriented/unoriented. Recently Scott Morrison and
Kevin Walker discovered that in order to make Khovanov homology work
nicely one should work with a new flavor of Temperley-Lieb which they
call "disoriented." I'll explain where the difference between
unoriented and disoriented comes from, relate this to the
Frobenius-Schur indicator, and explain that there's a subtle
difference between U_q(sl_2) at roots of unity and the A_n Subfactors.
This is joint work with Peter Tingley.
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Speaker: Alan Wiggins
Title: Strong Singularity for Subfactors
Abstract: TBA
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Speaker: Feng Xu
Title: Introduction to intermediate subfactor lattice
Intermediate subfactor lattice and conformal field theory (I)
Intermediate subfactor lattice and conformal field theory (II)
Abstract: TBA
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