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                                                                                        Research

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Most of my current research centers around the application of operator algebras and tensor categories to problems in quantum physics, particularly in the contexts of quantum information, quantum many-body physics and topologically ordered phases of matter. Other interests include TQFTs, higher categories, subfactors, and representation theory. I am also interested in related philosophical questions in the foundations of physics, and the relationship between mathematics and the physical world. 

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-My research is currently supported by NSF Grant DMS- 2247202. 

 

-From 2019-2023, by research was supported by NSF Grant DMS-2100531 (transfer from DMS-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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  • Quantum cellular automata and categorical dualities of spin chains (with Kylan Schatz and Dominic J. Williamson). arXiv: 2410.08884

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  • Quantum symmetries of noncommutative tori. (with David E. Evans). arXiv:2404.14466

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  • Levin-Wen is a gauge theory: entanglement from topology (with Kyla Kawagoe, Sean Sanford, David Green, and David Penneys). Comm. Math. Phys. arXiv:2401.13838

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  • Equivariant D-stability for actions of tensor categories (with Samuel Evington and Sergio Girón Pacheco). arXiv: 2401.14238

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  • An index for quantum cellular automata on fusion spin chains (with Junhwi Lim). Annales Henri Poincaré. arXiv:2309.10961

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  • ​​Local topological order and boundary algebras (with David Penneys, Pieter Naaijkens, and Daniel Wallick). arXiv:2307.12552

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  • ​​​DHR bimodules of quasi-local algebras and symmetric quantum cellular automata. Accepted to Quantum Topology (special issue dedicated to Vaughan Jones)  arXiv:2304.00068

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  • Unitary connections on Bratteli diagrams (with Paramita Das, Shamindra Ghosh, and Mainak Ghosh). Journal of Topology and Analysis (2023). arXiv:2211.03822

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  • Composing topological domain walls and anyon mobility (with Peter Huston, Fiona Burnell, and David Penneys). SciPost Physics (2023). arXiv:2208.14018

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  • K-theoretic classification of inductive limit actions of fusion categories on AF-algebras. (with Quan Chen and Roberto Hernández Palomares). Comm. Math. Phys. arXiv:2207.11854  

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  • Equivariant fusion subcategories. (with César Galindo). Transformation Groups (2024). arXiv:2111.09116  

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  • A categorical Connes' 𝛘(M) (with Quan Chen and David Penneys). Math. Ann. (2023). arXiv:2111.06378 

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  • Q-system completion for C* 2-categories (with Quan Chen, Roberto Hernández Palomares and David Penneys).  J. Funct. Anal. (2022).  arxiv:2105.12010 

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  • Remarks on anomalous symmetries of C*-algebras. Comm. Math. Phys. (2021).  arxiv:2011.13898

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  • A 3-categorical perspective on G-crossed braided categories (with David Penneys and David Reutter).  J. London Math. Soc. (2023). 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).  Int. Math. Res. Not. (2022). arxiv:1910.03178

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  • Computing fusion rules for spherical G-extensions of fusion categories (with Marcel Bischoff). Selecta Math (2022).  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). 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), 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 workshops/conferences:

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1). Topological invariants of symmetric quantum cellular automata, BIRS, Banff, CA (video)

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2). Quantum cellular automata on fusion categorical spin chains, ICMS Edinburgh, UK (video)

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3). K-theoretic classification of inductive limit actions of fusion categories on AF-algebras, HIM Bonn, DE (video)

 

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

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5). Spontaneous symmetry breaking from anyon condensation, BIRS, Banff CA (video)

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

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PhD Students:

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Emily McGovern

Sean Thompson

Kylan Schatz

Ali Elokl

Alex Betz

Noah Lanier

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