Fall 2018

- Date:
**8/31/18****Cain Edie-Michell, Vanderbilt University**- Title: Classifying small dimension bimodules of the hyperfinite type II_1 factor.
- Abstract: While the classification of modules over the hyperfinite type II_1 factor has long been known, the situation with bimodules is still far from being well understood. One of the few results in this direction is the classification of self-dual bimodules of Von Neumann-Murray dimension less than 2. Such bimodules are classified by the ADET Dynkin diagrams. In recent work I have been able to extend this classification, relaxing the condition that a bimodule M be self-dual, to just requiring that M commutes with its dual under the Connes tensor product. Along with the expected ADET bimodules, we find interesting and exotic new examples, such as a "twisted E_6" bimodule, along with many others.

- Date:
**9/7/18****Pieter Spaas, UC San Diego**- Title: II_1 factors with a unique McDuff decomposition.
- Abstract: We consider McDuff decompositions of II_1 factors. In particular, we will discuss a structural result for such a decomposition, when the central sequences of the non-McDuff part are captured by a Cartan subalgebra. This will allow us to deduce several new instances where the involved II_1 factor admits a unique McDuff decomposition. We will also comment on some related properties and results for equivalence relations.

- Date:
**9/14/18****Ben Hayes, University of Virginia**- Title: Pinsker algebras for 1-bounded entropy.
- Abstract: I will discuss the notion of a Pinkser algebra for 1-bounded entropy (a modification of free entropy dimension for strongly 1-bounded algebras in the sense of Jung). Given a tracial von Neumann algebra M, a Pinsker algebra in M is a subalgebra P of M which is maximal with respect to the property that the 1-bounded entropy of P in M is zero. Such algebras always exist. I will discuss properties of Pinkser algebras, as well as give at least one interesting example of such an algebra, and discuss the difficulties involved in producing more examples.

- Date:
**9/28/18****Noah Snyder, Indiana University**- Title: Module categories, graph planar algebra embeddings, and Extended Haagerup
- Abstract: A natural question that Pinhas Grossman and I have been studying is given a finite collection of finite index N-N bimodules what are all factors M containing N which can be built as a sum of these bimodules. This question is closely related to several "representation theoretic" questions about fusion categories, namely classifying module categories, finding Ocneanu's "maximal atlas", and finding Etingof-Nikshych-Ostrik's "Brauer-Picard groupoid." Unrelated to all of this, Vaughan Jones asked given a fixed subfactor planar algebra P, can you find all bipartite graphs \Gamma such that P embeds into the Graph Planar Algebra of \Gamma. Emily Peters gave partial evidence that for the Haagerup subfactor there were exactly three such graphs (the two principal graphs, and the broom). My main goal in this talk is to explain why these two questions are basically the same as each other. The key result is a GPA embedding theorem for module categories, which says that P embeds in the GPA(\Gamma) if and only if \Gamma is the fusion graph for some module category. In particular, I will show that it follows from my first paper with Pinhas that Emily's three graphs are the only graphs with Haagerup GPA embeddings. We are also able to use this approach to answer all these questions for the Extended Haagerup subfactor, showing that there are two new fusion categories EH3 and EH4 which still appear to be exceptional. This is joint work with Grossman, Morrison, Penneys, and Peters as part of our AIM Square.

- Date:
**10/5/18****Scott Atkinson, Vanderbilt University**

- Date:
**10/12/18****Corey Jones, Ohio State University**

- Date:
**10/19/18****No Meeting, Fall Break.**

- Date:
**10/26/18****Josh Edge, Indiana University**

- Date:
**Monday 10/29/18, 4:10-5:30pm****Paramita Das, Indian Statistical Institute**

- Date:
**11/2/18, 4:10-5:00pm****Shamindra Ghosh, Indian Statistical Institute**

- Date:
**11/9/18****Yasu Kawahigashi, University of Tokyo**

- Date:
**11/16/18** - Date:
**11/23/18****No Meeting, Thanksgiving Break.**

- Date:
**11/30/18** - End of Fall Semester.

Some related conferences/workshops this semester: