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. ______________________________________________________________________________________ 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 classi cation 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. ______________________________________________________________________________________ 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. ______________________________________________________________________________________ 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. ______________________________________________________________________________________ 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. ______________________________________________________________________________________ Speaker: Vaughan Jones Title: Pairs of finite index subfactors, systems of bimodules and II_1 factors coming from graded algebras Abstract: TBA ______________________________________________________________________________________ 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. ______________________________________________________________________________________ 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! ______________________________________________________________________________________ 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. ______________________________________________________________________________________ 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 $LG$. ______________________________________________________________________________________ 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. ______________________________________________________________________________________ Speaker: Alan Wiggins Title: Strong Singularity for Subfactors Abstract: TBA ______________________________________________________________________________________ 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 ______________________________________________________________________________________