The TACO seminar focuses on topics in Topology, Algebra, Combinatorics, and Operators.
Date | Speaker | Title |
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Sep 3 | Tony Giaquinto Loyola University Chicago |
The center of the Temperley-Lieb algebra [abstract] |
Abstract |
We present a uniform description of the center of the Temperley–Lieb algebra \(TL_n(\delta)\) for all nonzero complex parameters \(\delta\). In particular, we show that the center has dimension \[dim(Z(TL_n(\delta)) = 1 +\lfloor\frac{n}{2}\rfloor\] for every\(n\) and \(\delta\), and we describe a basis arising from a natural filtration closely tied to the cellular structure of \(TL_n(\delta)\). Our approach makes use of the diagrammatic and algebraic presentation of Temperley–Lieb algebras, their representation theory, and deformation theoretic methods. |
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Sep 10 | Aaron Lauve Loyola University Chicago |
Adjoint modalities in combinatorial (Hopf) algebras [abstract] |
Abstract |
In studying Hopf algebras \(H=\bigoplus_{n\geq0} \mathbb{Z}P_n\) built on combinatorial gadgets \(P_\bullet\) with a natural poset structure, it is natural (and often fruitful) to use the poset to define new bases for \(H\). Here I introduce a variation on the common technique in the presence of poset maps \(f_n:P_n \to Q_n\). After introducing the basic framework, I'll give several examples and a couple consequences. As the title suggests, the former requires the maps \(f_n\) to be part of an *adjoint modality. Based on joint work with Marcelo Aguiar. (In progress.). |
Sep 24 | Daniel Wallick The Ohio State University |
Superselection sectors for a poset of von Neumann algebras [abstract] |
Abstract |
The notion of superselection sectors has appeared often in algebraic quantum field theory and has been adapted to various settings, including conformal nets and quantum spin systems. Here, we describe a general mathematical framework that describes quantum spin systems and conformal nets. Specifically, we define a net of von Neumann algebras associated to a poset and define superselection sectors corresponding to that net. We show that if the poset satisfies geometric axioms, then the superselection sectors form a braided monoidal category. This is joint work with Anupama Bhardwaj, Tristen Brisky, Chian Yeong Chuah, Kyle Kawagoe, Joseph Keslin, and David Penneys.. |
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Oct 8 | Lucas Gagnon University of Southern California |
TBD [abstract] |
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Here is where the abstract will appear. |
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Oct 22 | Javid Validashti DePaul University |
TBD [abstract] |
Abstract |
Here is where the abstract will appear. |
Oct 29 | Jonah B Gaster UW Milwaukee |
Title TBD [abstract] |
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Nov 5 | Amanda Redlich UMass Lowell |
TBD [abstract] |
Abstract |
Here is where the abstract will appear. |
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Nov 12 | Williem Rizer University of Kentucky |
TBD [abstract] |
Abstract |
Here is where the abstract will appear. |
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