Research | Corey Jones Math

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 DMS-2100531 (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

K-theoretic classification of inductive limit actions of fusion categories on AF-algebras. (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

Q-system completion for C* 2-categories (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 3-categorical perspective on G-crossed 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 braided-enriched fusion categories (with Scott Morrison, David Penneys, and Julia Plavnik). Int. Math. Res. Not. arxiv:1910.03178

Computing fusion rules for spherical G-extensions of fusion categories (with Marcel Bischoff). Selecta Math. 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). To appear in 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), 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 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 recordings of talks I've given at some conferences:

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

2). A survey of G-crossed 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)