• Date: 9/5/25
  • Dietmar Bisch, Vanderbilt University
  • Title: Subfactors yearn for Analysis
  • Abstract: The representation theory of an inclusion of II_1 factors with finite Jones index, also called a subfactor, is a unitary tensor category of bimodules. If the subfactor is hyperfinite, and the category is fusion, it classifies the subfactor by a result of Popa. However, this is a rather special situation, and analysis is required in general to understand the subfactor.

    I will explain all these notions and show explicit examples of hyperfinite subfactors arising from actions of property (T) groups that have different analytical properties, but the representation categories are the same.

• Date: 9/12/25
  • Darren Creutz, Vanderbilt University
  • Title: Harmonic Functions on Compactly Generated Groups
  • Abstract: Implicit in the work of Mok (1995) and Kleiner (2010 is the statement that a finitely generated group is infinite if and only if there exists a nonconstant harmonic function on the group for any (equivalently every) reasonable probability measure on the group.  I will present (sort of) recent work generalizing this to locally compact second countable compactly generated groups: such a group is noncompact if and only if it admits a nonconstant Lipschitz-bounded harmonic function (for any/every reasonable probability measure).  The proof involves Margulis' technique of amenability+(T) as well as Mok/Kleiner's energy argument.  The property (T) half of the proof is joint work with Y. Shalom.

• Date: 9/19/25
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• Date: 9/26/25
  • Junhwi Lim, Vanderbilt University
  • Title: Planar algebras associated to cocommuting squares
  • Abstract: The ‘generalized symmetries’ of subfactors are encoded by their planar algebras. A natural foundational question is “What minimal structure can be universally expected from these symmetries?” For arbitrary subfactors, Jones showed that the associated planar algebra contains the Temperley-Lieb-Jones algebra. When an intermediate subfactor is present, the planar algebra contains the Fuss-Catalan-Bisch-Jones algebra, introduced by Bisch and Jones. However, the situation with two intermediate subfactors remains an open problem. As a natural special case, we study cocommuting squares of factors with ‘group-like’ properties. We exhibit the skein relations of their associated planar algebras and show that these algebras extend the partition algebras. This is based on a joint work with Dietmar Bisch.

• Date: 10/3/25
  • Yoonkyeong Lee, Michigan State University
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• Date: 10/10/25
  • No Meeting, Fall Break

• Date: 10/17/25 **Zoom Meeting**
  • Jinson Wu, Beijing Institute of Mathematical Sciences and Applications (BIMSA)
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• Date: 10/24/25
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• Date: 10/31/25
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• Date: 11/7/25
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• Date: 11/14/25
  • Srivatsav Kunnawalkam Elayavalli, University of Maryland
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• Date: 11/21/25
  • no meeting (tentative)
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• Date: 11/28/25
  • No Meeting, Thanksgiving Break

• End of Fall Semester.

Past NCGOA and Subfactor seminars