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8/28/23, 9:00 AM
Based on a graphical calculus for pivotal bicategories, we develop a string-net construction of a modular functor. We show that a rigid separable Frobenius functor between strictly pivotal bicategories induces a linear map between the corresponding bicategorical string-net spaces that is compatible with the mapping class group actions and with sewing. This result implies that correlators of...
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8/28/23, 10:15 AM
’t Hooft anomalies are obstructions to gauging a global symmetry of a QFT. In one spatial dimension ’t Hooft anomaly of a Lie group symmetry can also be described purely algebraically, without a reference to gauging: it manifests itseld a non-trivial central extension of the current algebra. In higher dimensions, there is no completely satisfactory algebraic reformulation of ’t Hooft anomaly....
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8/28/23, 11:15 AM
In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved...
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8/28/23, 4:45 PM
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8/29/23, 9:00 AM
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8/29/23, 10:15 AM
My talk is about how categorical symmetries act on and organise the spectrum of non-topological extended operators in QFT. I will address this question from two equivalent perspectives: the representation theory of higher tube algebras and the sandwich construction of symmetries via the Drinfeld center. I'll discuss a variety of examples in three dimensions: invertible symmetries and higher...
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8/29/23, 11:15 AM
This talk will be on recent joint work with Robert Laugwitz and Milen Yakimov (arXiv:2307.14764) that is motivated by obtaining solutions to the quantum reflection equation (qRE). To start, given a braided monoidal category C and C-module category M, we introduce a version of the Drinfeld center Z(C) of C adapted for M. We refer to this category as the "reflective center" E_C(M) of M. Just...
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8/29/23, 5:45 PM
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8/30/23, 9:00 AM
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8/30/23, 10:15 AM
We define a Turaev-Viro-Barrett-Westbury state sum model of triangulated 3-manifolds with surface defects (oriented 2d surfaces), line defects and point defects (graphs on the defect surfaces). Surface defects are labeled with bimodule categories over spherical fusion categories with bimodule traces, line and point defects with bimodule functors and
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bimodule natural transformations. The state... -
8/30/23, 11:15 AM
I will give a summary of recent works on global categorical symmetries in QFTs, with a focus on non-invertible symmetries and their description in terms of fusion higher categories. In addition to discussing the symmetries, I will also introduce the notion of a generalized charge, and provide several examples of this for both invertible and non-invertible symmetries.
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8/31/23, 9:00 AM
Factorization algebras arose in topology and representation theory but also provide a framework for describing the observables and symmetries of a field theory. This talk will begin by surveying factorization algebras and what they do well -- and do not -- in physics, at least at present. In the latter part we will describe work in progress with Araminta Amabel on selection rules for line...
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8/31/23, 10:15 AM
We consider ’t Hooft anomalies for a variety of 4d gauge theories whose fermion matter content admits Spin_G(4) generalized spin structure, with G gauged or global.
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We discuss and compute the w2 w3 type ’t Hooft anomalies that arise in this context, and aspects of anomaly matching in the possible IR phases. Based on work with T. Daniel Brennan. -
8/31/23, 11:15 AM
Any (n-pivotal) n-category C can be embedded in a Morita-equivalent completion C^#. Because of the Morita equivalence, any module/action of C automatically leads to one of the larger category C^#. In particular, discrete k-form symmetries of d-dimensional QFTs correspond to actions of C(G, d+1, k+1) = \pi_{\le d+1}(B^{k+1}(G)), and therefore give rise to actions of the completed...
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8/31/23, 5:45 PM
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9/1/23, 9:00 AM
The no-bordism conjecture by McNamara and Vafa states that the bordism group with tangential structure and branes (singularity types) for a consistent quantum gravity should vanish.
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This predicted previously unknown non-supersymmetric branes in string theory which should cancel the apparently nontrivial bordism classes.
In this talk I will propose the worldsheet theories of a string in the... -
9/1/23, 10:15 AM
In this talk, I will motivate derived Skein modules, which recover (classical) Skein modules while possessing a host of expected continuous symmetries, functorialities, and local-to-global formulae. Then, using factorization homology, I will outline how to construct derived Skein modules.
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9/4/23, 9:00 AM
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9/4/23, 10:15 AM
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9/4/23, 11:15 AM
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9/4/23, 3:30 PM
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9/4/23, 5:00 PM
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9/5/23, 9:00 AM
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9/5/23, 10:15 AM
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9/5/23, 11:15 AM
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9/5/23, 3:30 PM
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9/5/23, 5:00 PM
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9/5/23, 6:00 PM
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9/5/23, 8:00 PM
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9/6/23, 9:00 AM
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9/6/23, 10:15 AM
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9/6/23, 11:15 AM
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9/6/23, 5:00 PM
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9/6/23, 6:00 PM
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9/7/23, 9:00 AM
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9/7/23, 10:15 AM
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9/7/23, 11:15 AM
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9/7/23, 5:00 PM
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9/7/23, 6:00 PM
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9/8/23, 9:00 AM
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9/8/23, 10:15 AM
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9/8/23, 11:15 AM
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