Research
-My main research interests are in quantum algebra. In particular, I study tensor categories, representation theory and higher categories. Questions I am interested in are often motivated by applications in mathematical physics (topological phases of matter, conformal field theory, topological quantum field theory) or operator algebras (subfactors, compact quantum groups, noncommutative geometry).
-My research is supported by NSF Grant DMS-2100531 (previously 1901082).
-Here is a link to my Google Scholar page.
Publications and Preprints:
1). A 3-categorical perspective on G-crossed braided categories (with David Penneys and David Reutter). arxiv:2009.00405
2). Triangle presentations and tilting modules for SL2k+1. arxiv:2005.07172
3). Extension theory for braided-enriched fusion categories (with Scott Morrison, David Penneys, and Julia Plavnik). arxiv:1910.03178
4). Computing fusion rules for spherical G-extensions of fusion categories (with Marcel Bischoff). arxiv:1909.02816
5). 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
6). Spontaneous symmetry breaking from anyon condensation (with Marcel Bischoff, Yuan-Ming Lu, and David Penneys). J. High Energ. Phys. (2019). , arxiv:1811.00434
7). 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
8). 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
9). Vanishing of categorical obstructions for permutation orbifolds (with Terry Gannon). Comm. Math. Phys. (2019). , arXiv:1804.08343
10). 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
11). Annular representations of free product categories (with Shamindra Kumar Ghosh and Madhav B. Reddy). To appear in J. Noncommut. Geom. arxiv:1803.06817
12). Fusion rules for Z/2Z permutation gauging (with Cain Edie-Michell and Julia Plavnik). To appear in J. Math Phys. arXiv:1804.01657
13). Q-systems and compact W*-algebra objects (with David Penneys), to appear in a volume of Contemporary Mathematics series. arXiv:1707.02155
14). Realizations of algebra objects and discrete subfactors (with David Penneys). Adv. Math. (2019). arXiv:1704.02035
15). Operator algebras in rigid C*-tensor categories (with David Penneys). Comm. Math.
Phys. (2017). , arxiv: 1611.04620
16). Classification of Thurston-relation subfactor planar algebras (with Zhengwei Liu and Yunxiang Ren). To appear in Quantum Topol. arxiv:1606.00779
17). Eigenvalues of rotations and braids in spherical fusion categories (with Daniel Barter and Henry Tucker). J. Algebra (2018), , arxiv:1611.00071
18). Quantum G2 categories have property (T). Internat. J. Math. 27 (2016), no. 2, 1650015. MR3464395. arXiv: 1504.08338
19). 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
20). 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
Recorded Talks:
Here are links to recordings of talks I've given at some conferences:
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)