Research

​

​

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 many-body physics, quantum field theory and topologically ordered phases of matter. Other interests include 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. 

​

​

-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).

​

-Here is a link to my Google Scholar page.

​​

​

​

Publications and Preprints:​​​​

​​

 

• An operator algebraic approach to fusion category symmetry on the lattice (with David E. Evans). arXiv: 2507.05185.

​

• Holography for bulk-boundary local topological order (with David Penneys and Pieter Naaijkens). arXiv: 2506.19969.

​​​​​​

• On the structure of DHR bimodules of abstract spin chains (with Lucas Hataishi, David Jaklitsch, Makoto Yamashita). arXiv: 2504.06094

​

• Universal coarse geometry of spin systems (with Ali Elokl). Letters in Mathematical Physics. arXiv: 2411.07912.

​

• Quantum cellular automata and categorical dualities of spin chains (with Kylan Schatz and Dominic J. Williamson). arXiv: 2410.08884

​

• Quantum symmetries of noncommutative tori. (with David E. Evans). Communications in Mathematical Physics (special issue dedicaticated to Huzihiro Araki) arXiv:2404.14466

​​

• 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

​

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

​

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

​

• ​​Local topological order and boundary algebras (with David Penneys, Pieter Naaijkens, and Daniel Wallick). Accepted to Forum of Mathematics, Sigma. arXiv:2307.12552

​

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

​

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

​

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

​

• 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  

​

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

​

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

​

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

​

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

​

• A 3-categorical perspective on G-crossed braided categories (with David Penneys and David Reutter).  J. London Math. Soc. (2023). arxiv:2009.00405

​

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

​

• Extension theory for braided-enriched fusion categories (with Scott Morrison, David Penneys, and Julia Plavnik).  Int. Math. Res. Not. (2022). arxiv:1910.03178

​

• Computing fusion rules for spherical G-extensions of fusion categories (with Marcel Bischoff). Selecta Math (2022).  arxiv:1909.02816 

​

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

​

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

​

• 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

​

• 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

​

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

​

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

​

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

​

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

​

• Q-systems and compact W*-algebra objects (with David Penneys), Contemporary Mathematics series. arXiv:1707.02155 

​

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

​

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

​

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

​

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

​

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

​

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

​

• 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​​

​

​

​

                           

 

Recorded Talks:

​

Here are links to (recentish) recordings of talks I've given at some workshops/conferences/seminars:

​

1). Quantum cellular automata on fusion spin chains, Kadanoff Center for Theoretical Physics, University of Chicago (video)

​

2). Holographic principle for local topological order, IMSA, University of Miami (video)

​

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

​

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

​​

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

​​​

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

​

​​

​

​

​

(Current and Former) PhD Students:

​

Emily McGovern

Sean Thompson

Kylan Schatz

Ali Elokl

Alex Betz

Noah Lanier

Ian Bunner

​

​