Research

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-My main interests concern algebraic structures that arise in, or are motivated by, quantum physics. In particular, I study tensor categories, operator algebras, higher categories, and representation theory. Questions I think about are typically inspired by concepts of quantum symmetry.

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-My research is supported by NSF Grant DMS-2100531 (previously 1901082).

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-Here is a link to my Google Scholar page.

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Publications and Preprints:

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  • Q-system completion for C* 2-categories (with Quan Chen, Roberto Hernández Palomares and David Penneys). To appear in J. Funct. Anal.  arxiv:2105.12010 

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  • Remarks on anomalous symmetries of C*-algebras. To appear in Comm. Math. Phys.  arxiv:2011.13898

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  • A 3-categorical perspective on G-crossed braided categories (with David Penneys and David Reutter). arxiv:2009.00405

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  • Triangle presentations and tilting modules for SL2k+1. J. Comb. Algebra. (2021). arxiv:2005.07172

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  • Extension theory for braided-enriched fusion categories (with Scott Morrison, David Penneys, and Julia Plavnik). To appear in Int. Math. Res. Not. arxiv:1910.03178

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  • Computing fusion rules for spherical G-extensions of fusion categories (with Marcel Bischoff). To appear in Selecta Math.  arxiv:1909.02816 

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  • Rank-finiteness for G-crossed braided fusion categories (with Scott Morrison, Eric C. Rowell, and Dmitri Nikshych).  Transform. Groups. (2020). arxiv:1902.06165 

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  • Spontaneous symmetry breaking from anyon condensation (with Marcel Bischoff, Yuan-Ming Lu, and David Penneys).  J. High Energ. Phys. (2019).  arxiv:1811.00434

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  • Fusing binary interface defects in topological phases: the Vec(Z/pZ) case (with Daniel Barter and Jacob C. Bridgeman). To appear in J. Math. Phys. (2019).  arxiv: 1810.09469

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  • Domain walls in topological phases and the Brauer-Picard ring for Vec(Z/pZ)  (with Daniel Barter and Jacob C. Bridgeman). Comm. Math. Phys. (2019). arxiv: 1806.01279

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  • Vanishing of categorical obstructions for permutation orbifolds (with Terry Gannon). Comm. Math. Phys. (2019).  arXiv:1804.08343

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  • Free oriented extensions of subfactor planar algebras (with Shamindra Kumar Ghosh and Madhav B. Reddy).  Internat. J. of Math.  (2018). arXiv:1805.08971

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  • Annular representations of free product categories (with Shamindra Kumar Ghosh and Madhav B. Reddy). J. Noncommut. Geom. (2020). arxiv:1803.06817

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  • Fusion rules for Z/2Z permutation gauging (with Cain Edie-Michell and Julia Plavnik).  J. Math Phys. (2019). arXiv:1804.01657

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  • Q-systems and compact W*-algebra objects (with David Penneys), to appear in a volume of Contemporary Mathematics series. arXiv:1707.02155 

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  • Realizations of algebra objects and discrete subfactors (with David Penneys). Adv. Math. (2019).  arXiv:1704.02035

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  • Operator algebras in rigid C*-tensor categories (with David Penneys). Comm. Math. Phys. (2017).  arxiv: 1611.04620

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  • Classification of Thurston-relation subfactor planar algebras (with Zhengwei Liu and Yunxiang Ren).  Quantum Topol. (2019). arxiv:1606.00779 

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  • Eigenvalues of rotations and braids in spherical fusion categories (with Daniel Barter and Henry Tucker). J. Algebra (2018). arxiv:1611.00071

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  • Quantum G2 categories have property (T). Internat. J. Math. (2016). arXiv: 1504.08338

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  • Annular representation theory for rigid C*-tensor categories (with Shamindra Kumar Ghosh).  J. Funct. Anal. (2016). arXiv:1502.06543

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  • Discrete homotopy theory and critical values of metric space (with Jim Conant, Victoria Cur- nutte, Conrad Plaut, Kristen Pueschel, Maria Lusby, and Jay Wilkins). Fund. Math. (2014). arXiv:1205.2925​​

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Recorded Talks:

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Here are links to recordings of talks I've given at some conferences:

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1). A survey of G-crossed braided fusion categories, Simons Center for Geometry and Physics, Stony Brook, NY​ (video)

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2). Spontaneous symmetry breaking from anyon condensation, Banff International Research Station, CA (video)

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3). Operator Algebras in Rigid C*-tensor Categories, Isaac Newton Institute, Cambridge, UK (video)

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