Organizer(s) : Sayan Das
Description: The Student Subfactor Seminar is a platform for Graduate students at Vanderbilt to share their ideas and work on Subfactor theory. The topics of the talk could range from elementary introduction to the Subfactor theory, or talks on some recent works.
The idea is to build an interactive platform to learn Subfactor theory from one another, rather than learning alone- which is never much fun.
Schedule of Talks:
1) Monday April 1 (SC 1227 from 2:30 -4:00 p.m): Sayan Das : On Temperley-Lieb Planar Algebras.
Abstract: In this talk we shall focus on the most basic example of a Planar Algebra, namely the Temperley-Lieb Planar Algebra. The talk will contain a basic introduction to Planar Algebras as well.
2) Wednesday April 3 (SC 1227 From 3:30- 5:00 P.M.) : Yunxiang Ren: Embedding Theorem for Graph Planar Algebras.
Abstract: In this talk we shall prove that every subfactor planar algebra embeds in the Graph planar algebra of its pricipal graph, and its generalization (as done by Scott Morrison and Kevin Walker). This talk will start from basic definitions, and will be accessible to anyone interested in subfactors or planar algebras.
3) Monday April 8 (SC 1404 From 3:30- 5:00 p.m.) Corey Jones: Group Planar Algebras.
Abstract: We will review the basic construction for group type subfactors, and describe the planar algebra of the standard invariant via generators and relations. We will also discuss the annular modules of these planar algebras.
4) Monday Sept 23 (SC 1404 From 3:00- 5:00 p.m.) Zhengwei Liu: Applications of Wenzl's formula.
Abstract: We will talk about Wenzl's formula and its general form. We will see its applications to other subfactor concepts, like Jellyfish, spoke subfactors, the embedding theorem, normalizers.
5) Monday Sept 30 (SC 1404 From 3:00- 5:00 p.m.) James Tener (U C Berkeley): Relationships between different definitions of corformal field theory.
Abstract: We will introduce three mathematical structures intended to capture the notion of a conformal field theory: conformal nets, vertex operator algebras, and Segal CFT. We will discuss the (philosophical) relationship between these different structures, as well as ongoing work to produce examples and theorems that implement these relationships.
6) Monday Oct. 21 (SC 1404 From 3:00- 5:00 p.m.) Chenxu Wen (Vanderbilt University): Unique Cartan subalgebras and solidity results for II_1 factors.
Abstract: The recent development in the rigidity results in the study of II_1 factors from the group-measure-space construction has lead to many new insights to the structure of certain factors. Of particular importance in the theory is the unique Cartan subalgebra (or group-measure-space Cartan), up to unitary conjugacy, for some II_1 factors. In the talk we will discuss the work in this direction started by Ozawa and Popa and followed by many others. As the consequence of the techniques involved, we will also talk about some solidity results for some group von Neumann algebras.