Zassenhaus Assistant Professor (NTT)
Department of Mathematics
The Ohio State University
I study quantum symmetries in the form of tensor categories, higher categories and their applications in topological phases of matter, conformal field theory and operator algebras.
I am currently a postdoc at the Ohio State University, with faculty mentor David Penneys. Previously I was a postdoc at the Australian National University under the supervision of Scott Morrison (2016-2018). I completed my PhD at Vanderbilt University under the supervision of Vaughan Jones in 2016. I'm originally from Raleigh, NC.
While much of my research is specifically focused on tensor categories and their applications, more broadly my interests include representation theory, higher categories, topological phases of matter, conformal field theory, subfactors, quantum groups and noncommutative geometry.
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. Groups. arxiv:1902.06165
4). Spontaneous symmetry breaking from anyon condensation (with Marcel Bischoff, Yuan-Ming Lu, and David Penneys). J. High Energ. Phys. (2019). , arxiv: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). , arxiv: 1806.01279
7). Vanishing of categorical obstructions for permutation orbifolds (with Terry Gannon). Comm. Math. Phys. (2019). , 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). , 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
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
Here are links to videos of talks I've given at conferences that have been recorded:
1). 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)