Research

I study tensor categories. I'm especially interested in their general structure, interactions with higher categories, and applications in mathematical physics and operator algebras. 

 

Things I tend to think about are usually related to: representation theory, topological phases of matter, subfactors, planar algebras, conformal field theory, or quantum groups.

-My research is supported by NSF Grant DMS-1901082.

-Here is a link to my Google Scholar page.

Publications and Preprints:

1). Extension theory for braided-enriched fusion categories (with Scott Morrison, David Penneys, and Julia Plavnik). arxiv:1910.03178

2). Computing fusion rules for spherical G-extensions of fusion categories (with Marcel Bischoff).  arxiv:1909.02816 

3). Rank-finiteness for G-crossed braided fusion categories (with Scott Morrison, Eric C. Rowell, and Dmitri Nikshych). To appear in Transform. Groupsarxiv:1902.06165 

4). Spontaneous symmetry breaking from anyon condensation (with Marcel Bischoff, Yuan-Ming Lu, and David Penneys).  J. High Energ. Phys. (2019). https://doi.org/10.1007/JHEP02(2019)062arxiv:1811.00434

5). 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.  arxiv: 1810.09469

6). 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). https://doi.org/10.1007/s00220-019-03338-2 , arxiv: 1806.01279

7). Vanishing of categorical obstructions for permutation orbifolds (with Terry Gannon). Comm. Math. Phys. (2019). https://doi.org/10.1007/s00220-019-03288-9 arXiv:1804.08343

8). Free oriented extensions of subfactor planar algebras (with Shamindra Kumar Ghosh and Madhav B. Reddy).  Internat. J. of Math. 29 (2018). no. 13, 1850093, arXiv:1805.08971

9). Annular representations of free product categories (with Shamindra Kumar Ghosh and Madhav B. Reddy). To appear in J. Noncommut. Geom. arxiv:1803.06817

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

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

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

13). Operator algebras in rigid C*-tensor categories (with David Penneys). Comm. Math.

Phys. (2017). https://doi.org/10.1007/s00220-017-2964-0 ,  arxiv: 1611.04620

14). Classification of Thurston-relation subfactor planar algebras (with Zhengwei Liu and Yunxiang Ren). To appear in Quantum Topol. arxiv:1606.00779 

15). Eigenvalues of rotations and braids in spherical fusion categories (with Daniel Barter and Henry Tucker). J. Algebra (2018), https://doi.org/10.1016/j.jalgebra.2018.08.011 , arxiv:1611.00071

16). Quantum G2 categories have property (T). Internat. J. Math. 27 (2016), no. 2, 1650015. MR3464395. arXiv: 1504.08338

17). Annular representation theory for rigid C*-tensor categories (with Shamindra Kumar Ghosh).

J. Funct. Anal. 270 (2016), no. 4, 1537–1584, MR3447719. arXiv:1502.06543

18). 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. 227 (2014), no.2, 97–128 MR3257953. arXiv:1205.2925​​