Fall 2025

• 08/20/2025 - Naihuan Jing (NC State)
  Title: q-immanants and Capelli identities
  Abstract: Capelli identity is a classical identity about the central elements of the enveloping algebra gl(n). It is one of the main tools in Weyl's famous book on classical groups. Immanant of a square matrix A is a generalization of det(A) and per(A) introduced by Littlewood. In 1996, Okounkov found new basis elements in Z(U(gl(n)) using the quantum immanant of the generator matrix of U(gl(n)). In this talk, I will discuss my recent joint work with M. Liu and A. Molev on quantization of Okounkov's quantum immanants and quantum Capelli identities for the quantum enveloping algebra of gl(n). 
  
  

• 08/27/2025 - David Green (NC State)
  Title: Braidings for non-split Tambara-Yamagami Categories over the reals
  Abstract: Non-split Real Tambara-Yamagami categories are a family of fusion categories over the real numbers that were recently introduced and classified by Plavnik, Sanford, and Sconce. Owing to the fact that the reals are not algebraically closed, these categories involve nontrivial division algebras along with interesting complex conjugation actions. Extending the work of Siehler, we consider which of these categories admit braidings, and classify the resulting braided equivalence classes in terms of quadratic forms. This is recent joint work with Sean Sanford and Yoyo Jiang. 
  
  

• 09/03/2025 - Seth Sullivant (NC State)
  Title: Lattice supported distributions and graphical models
  Abstract:  For the distributions of finitely many binary random variables, we study the interaction of restrictions of the supports with conditional independence constraints. We prove a generalization of the Hammersley-Clifford theorem for distributions whose support is a natural distributive lattice: that is, any distribution which has natural lattice support and satisfies the pairwise Markov statements of a graph must factor according to the graph. While these results are about statistical models, the proof techniques come from combinatorics and algebraic geometry.  This is joint work with Thomas Kahle.
  
  

• 09/10/2025 - 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.

• 09/17/2025 - Alex Betz
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• 09/24/2025 - Francisco Ponce-Carrion
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• 10/01/2025 - Camryn Thompson
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• 10/08/2025 - Anna Shapiro
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• 10/15/2025 - Daniel Profili
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• 10/22/2025 - Avery St. Dizier
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• 10/29/2025 - Michael Brown
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• 11/05/2025 - Ian Klein
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• 11/12/2025 - Tom Braden
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• 11/19/2025 - Karlee Westrem
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