### Papers/preprints

My arXiv author page | My Google Scholar page

- Classification of finite depth objects in bicommutant categories via anchored planar algebras [APA #4], submitted (with A. Henriques and D. Penneys)
- Unitary anchored planar algebras [APA #3], submitted (with A. Henriques and D. Penneys)
- Unitary vertex algebras and Wightman conformal field theories,
**Commun. Math. Phys.**395, 299–330 (2022) (with C. Raymond and Y. Tanimoto) - Fusion and positivity in chiral conformal field theory [GRACFT #3], submitted
- Classification of extremal vertex operator algebras with two simple modules,
**J. Math. Phys.**, 61 (2020), no. 5, 052302 (with J.C. Grady, CH. Lam, and H. Yamauchi) - Representation theory in chiral conformal field theory: from fields to observables [GRACFT #2],
**Selecta Math. (N.S.)**(2019), 25:76 - Positivity and fusion of unitary modules for unitary vertex operator algebras,
**RIMS Kôkyûroku**(2018), no. 2086, 6-13 - Singular values of weighted composition operators and second quantization,
**Int. Math. Res. Not.**(2018), no. 20, 6426-6441 (with M. Putinar) - On classification of extremal non-holomorphic conformal field theories,
**J. Phys. A: Math. Theor.**50 (2017) 115204 (with Z. Wang) - Geometric realization of algebraic conformal field theories [GRACFT #1],
**Adv. Math.**349 (2019), 488-563 - Construction of the unitary free fermion Segal CFT,
**Commun. Math. Phys.**355 (2017), no. 2, 463-518 - Planar algebras in braided tensor categories [APA #2],
**Mem. Amer. Math. Soc.**282 (2023), no. 1392 (with A. Henriques and D. Penneys) - Categorified trace for module tensor categories over braided tensor categories [APA #1],
**Documenta Math.**21 (2016) 1089-1149 (with A. Henriques and D. Penneys) - Subfactors of index less than 5, part 4: vines,
**Int. J. Math.**23 (2012), no. 3, 1250017 (with D. Penneys). - Unitary equivalence to a complex symmetric matrix: low dimensions,
**Lin. Alg. Appl.**437 (2012), no. 1, 271-284 (with S.R. Garcia and D.E. Poore) - Unitary equivalence of a matrix to its transpose,
**J. Operator Theory**68:1 (2012), 179-203 (with S.R. Garcia). - Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames,
**Oper. Matrices**5 (2011) 139-155 (with J. Giol, L.V. Kovalev, D. Larson and N. Nguyen). - Unitary equivalence to a complex symmetric matrix: an algorithm
**J. Math. Anal. Appl.**341 (2008) 640-648.

### Other writing

- Construction of the unitary free fermion Segal conformal field theory, Dissertation, UC Berkeley, Spring 2014 (advised by Vaughan Jones)
- Unitary equivalence to a complex symmetric matrix, Undergraduate thesis, Pomona College, Spring 2008 (advised by Stephan Garcia)

### Theses supervised

- Invariants in the II1 subfactor theory of von Neumann algebras, by Yiming (Andy) Yin, ANU Honours (2021)
- The Classification of Extremal Vertex Operator Algebras of Rank 2, by J. Connor Grady, UCSB undergraduate honors thesis (2018)

### Selected talks and talk notes:

- Towards a unified framework for the mathematics of conformal field theory, Operator algebras and mathematical physics (Yasu Fest 60), University of Tokyo, July 2023
- Towards a unified framework for the mathematics of conformal field theory [slides], Australian and New Zealand Association of Mathematical Physics (ANZAMP) Annual Meeting, February 2022, via Zoom
- Quantum fields from Haag-Kastler nets in 2d chiral conformal field theory [slides], MATRIX workshop on 2D Supersymmetric Theories and Related Topics, Creswick, Australia (via Zoom), January 2022
- Conformal nets are geometric [slides], Vanderbilt University Subfactor Seminar, December 2021
- Introduction to Segal CFTs, with connections to VOAs and conformal nets [slides], IASM-BIRS workshop Subfactors, Vertex Operator Algebras, and Tensor Categories, Hangzhou, China (via Zoom), September 2021
- Introduction to the VOA/conformal net correspondence [slides], IASM-BIRS workshop Subfactors, Vertex Operator Algebras, and Tensor Categories, Hangzhou, China (via Zoom), September 2021
- Thin surfaces and finite-index subfactors in chiral conformal field theory, ANZ Geometry, Strings, and Fields Seminar, May 2021
- Finite-index subfactors and rational conformal field theory, Tokyo-Kyoto Operator Algebras Zoom Seminar, January 2021
- Fusion, positivity, and finite-index subfactors, Vanderbilt University Subfactor Seminar, Nashville, TN (via Zoom), November 2020
- Thin cobordisms and operator algebras in conformal field theory, Wales MPPM Seminar, Cardiff, UK (via Zoom), July 2020
- Segal CFTs [video], MSRI Introductory Workshop: Quantum Symmetries, Berkeley, CA, January 2020
- Fusion, positivity, and finite-index subfactors in chiral conformal field theory, Oberwolfach workshop Subfactors and Applications, Germany, October 2019
- What is a chiral Segal CFT?, Subfactors in Maui 2019, Maui, USA, July 2019 (organizer)
- A unified perspective on 2d chiral CFT, Simons Center workshop
*Operator Algebras and Quantum Physics*, Simons Center for Geometry and Physics, New York, USA, June 2019 - A unified perspective on 2d chiral conformal field theory, NCGOA/Shanks conference on
*Algebra and Geometry Quantized and Quantified*, Vanderbilt University, Nashville, USA, May 2019 - Subfactors from vertex operator algebras [video], BIRS program Fusion Categories and Subfactors, Banff, Canada, October 2018
- A positivity conjecture for unitary VOAs [slides, video], Casa Matemática Oaxaca program Geometric and Categorical Aspects of CFTs, Oaxaca, Mexico, September 2018
- Local observables as boundary values of vertex operator algebras, Algebraic Methods in Mathematical Physics, CRM Montreal, July 2018
- Analytic problems arising at the boundary of the semigroup of annuli, (Sub)Factors in Maui, Kihei, HI, May 2018
- Construction of unitary Segal CFTs, Mathematical Physics Seminar, Perimeter Institute, April 2018
- Classification problems for VOAs with small rank, AMS Southeastern Sectional meeting, Special Session on Advances in Operator Algebras, Vanderbilt University, April 2018
- Conformal field theories for modular tensor categories with small rank, AMS Spring Central Sectional meeting, Special Session on Quantum Symmetries, March 2018
- Geometric conformal field theory: what, why, and how, University of Arizona Mathematics Colloquium, February 2018
- The geometry of conformal nets, JMM Special session on Advances in Operator Algebras, San Diego, CA, January 2018
- Local observables as boundary values of vertex operator algebras, Workshop on Research on algebraic combinatorics and representation theory of finite groups and vertex operator algebras, Kyoto RIMS, December 2017
- Fusion of representations of affine Lie algebras and functorial conformal field theory, UC Davis Seminar on Algebra & Discrete Mathematics, November 2017
- Construction of Segal CFTs, AMS Western Sectional meeting, Special Session on Tensor Categories: Bridging Algebra, Topology, and Physics, UC Riverside, November 2017
- A geometric approach to constructing conformal nets, AMS Western Sectional meeting, Special Session on Advances in Operator Algebras, UC Riverside, November 2017
- Geometry of conformal nets, Shanks workshop on subfactors and applications, Vanderbilt University, October 2017
- The geometry of conformal nets & Construction of unitary Segal CFTs (2 talks), Ohio State University Quantum Algebra & Quantum Topology seminar, and Non-commutative geometry and operator algebras seminar, September 2017
- Four flavors of fusion, Quantum Symmetries: Subfactors and Planar Algebras, Maui, HI, July 2017
- Planar algebras: calculating with pictures, Claremont Colleges Mathematics Colloquium, April 2017
- Jones-Wassermann subfactors from vertex operator algebras, Workshop on Subfactors, higher geometry, higher twists and almost Calabi-Yau algebras, Isaac Newton Institute for Mathematical Sciences, March 2017
- Singular values of weighted composition operators and second quantization, Southeasern Analysis Meeting (SEAM) 2017, UT Knoxville, March 2017
- Segal CFT and conformal nets (2 lectures), Berkeley-Tokyo Autumn School on Quantum Field Theory and Subfactors, UC Berkeley, November 2016
- Geometric construction of conformal nets, ECOAS 2016, Loyola University, October 2016
- On classification of vertex operator algebras by their representation categories, Modular Categories--Their Representations, Classification, and Applications, Casa Matemática Oaxaca, August 2016
- Finite index subfactors from vertex operator algebras, Von Neumann Algebras workshop, Hausdorff Institute for Mathematics, Bonn, July 2016
- Complete rationality of some conformal nets from vertex operator algebras, Trimester seminar for Mathematics and Physics at the Crossroads program, INFN Frascati, June 2016
- Segal CFT at the boundary, The Mathematics of Conformal Field Theory, Australian National University, July 2015
- From Segal CFT to conformal nets, Oberwolfach workshop Subfactors and conformal field theory, March 2015
- Segal CFT at the boundary, NCGOA 2014, Vanderbilt University, May 2014
- Operator algebras and geometric conformal field theory, East Coast Operator Algebras Symposium, University of Cincinnati, October 2013
- Segal CFT and vertex operator algebras via bounded operators, Quarterly Seminar on Geometry and Topology, Utrecht University, June 2013
- Manifestly unitary conformal field theory, Miniworkshop on Operator Algebras II, University of Tokyo, January 16, 2013
- Introduction to fermionic second quantization, NCGOA 2012, Vanderbilt University, May 5, 2012
- Two-interval subfactors and the Longo-Rehren construction, UC Berkeley Subfactor Seminar, March 2011 (expository following Kawahigashi-Longo-Mueger)
- Classification of LG-reps and weight polytopes for the characters of LG-rep (expository), Workshop on Operator Algebras and Conformal Field Theory, U Oregon, August 17, 2010
- A direct proof of an irreducibilty result of Wassermann, UC Berkeley Subfactor Seminar, April 16, 2010
- Finite-dimensional von Neumann algebras and the basic construction (expository), UC Berkeley Student Subfactor Seminar, October 2009
- Unitary equivalence to a complex symmetric matrix, Pomona College Analysis Seminar, December 10, 2007

### Conferences co-organised

- The Mathematics of Conformal Field Theory II, Australian National University, July 2021
- Subfactors in Maui 2019, July 2019
- Workshop on Quantum Symmetries, ANU Kioloa Coastal Campus, February 2019
- Subfactors in Sydney, February 2019
- Quantum Symmetries: Subfactors and Planar Algebras , July 2017
- Subfactor Theory in Mathematics and Physics 2014, July 2014
- Subfactors in Maui 2013, July 2013
- QFTahoe Workshop 2013, March 2013
- Subfactors in Maui 2012, July 2012
- Subfactors in Tahoe 2012, February 2012