Research
Most of my work is in the general areas of quantum algebra and mathematical physics. The mathematical topics I think the most about are tensor categories, operator algebras, and higher algebra. Recently I have been very interested in using all of these tools to rigorously study quantum spin systems (which I think of as discrete quantum field theories) and topological order. I sometimes work on purely mathematical problems inspired by physics, but I also enjoy collaborating with physicists to develop and apply abstract mathematical tools to concrete physical problems.
My research is supported by NSF Grant DMS2100531 (previously 1901082).
Here is a link to my Google Scholar page.
Publications and Preprints:

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

Ktheoretic classification of inductive limit actions of fusion categories on AFalgebras. (with Quan Chen and Roberto Hernández Palomares). arXiv:2207.11854

Equivariant fusion subcategories. (with César Galindo). arXiv:2111.09116

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

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

Remarks on anomalous symmetries of C*algebras. Comm. Math. Phys. arxiv:2011.13898

A 3categorical perspective on Gcrossed braided categories (with David Penneys and David Reutter). To appear in J. London Math. Soc. arxiv:2009.00405

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

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

Computing fusion rules for spherical Gextensions of fusion categories (with Marcel Bischoff). Selecta Math. arxiv:1909.02816

Rankfiniteness for Gcrossed 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, YuanMing 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). To appear in J. Math. Phys. (2019). arxiv: 1810.09469

Domain walls in topological phases and the BrauerPicard 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 EdieMichell and Julia Plavnik). J. Math Phys. (2019). arXiv:1804.01657

Qsystems and compact W*algebra objects (with David Penneys), to appear in a volume of 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 Thurstonrelation 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 recordings of talks I've given at some conferences:
1). Ktheoretic classification of inductive limit actions of fusion categories on AFalgebras, HIM Bonn, DE (video)
2). A survey of Gcrossed braided fusion categories, Simons Center for Geometry and Physics, Stony Brook, NY (video)
2). Spontaneous symmetry breaking from anyon condensation, Banff International Research Station, CA (video)
3). Operator Algebras in Rigid C*tensor Categories, Isaac Newton Institute, Cambridge, UK (video)