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David Penneys
Professor of Mathematics at The Ohio State University Office: Room 752 Math Tower Email: penneys (dot) 2 (at) osu (dot) edu |
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About me:
I received my Ph.D. from the University of California, Berkeley in 2012 under the supervision of Vaughan Jones. I completed a 2 year postdoc from 2012-2014 at the University of Toronto under the supervision of Dror Bar-Natan and George Elliott. From 2014-2016, I was an Assistant Adjunct Professor at UCLA. I study subfactor theory, a subject in operator algebras with connections to a wide variety of mathematics, including tensor and fusion categories, quantum algebra, mathematical physics, and non-commutative geometry.
Here is a copy of my Curriculum Vitae.
Here is a link to my articles on the arXiv.
Here is a link to my Google Scholar profile.
I received my Ph.D. from the University of California, Berkeley in 2012 under the supervision of Vaughan Jones. I completed a 2 year postdoc from 2012-2014 at the University of Toronto under the supervision of Dror Bar-Natan and George Elliott. From 2014-2016, I was an Assistant Adjunct Professor at UCLA. I study subfactor theory, a subject in operator algebras with connections to a wide variety of mathematics, including tensor and fusion categories, quantum algebra, mathematical physics, and non-commutative geometry.
Here is a copy of my Curriculum Vitae.
Here is a link to my articles on the arXiv.
Here is a link to my Google Scholar profile.
Graduate students and postdocs
Current graduate students and their dissertation work
Current graduate students and their dissertation work
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David GREEN, GRADUATING 2025
- Tannaka-Krein reconstruction for fusion 2-categories. [arXiv:2309.05591]
- Levin-Wen is a gauge theory: entanglement from topology (with coauthors). Comm. Math. Phys. [arXiv:2401.13838, DOI:10.1007/s00220-024-05144-x]
- A lattice model for condensation in Levin-Wen systems (with coauthors). J. High Energy Phys. [arXiv:2303.04711 DOI:10.1007/JHEP09(2023)055]
- Enriched string-net models and their excitations (with coauthors). Quantum [arXiv:2305.14068]
- REU project: Classification of Rank 6 Modular Categories with Galois Group <(012)(345)>. [arXiv:1908.07128]
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Giovanni FERRER
- Manifestly unitary higher Hilbert spaces (with coauthors). [arXiv:2410.05120]
- Foundations for operator algebraic tricategories. [arXiv:2404.05193]
- Dagger n-categories (with coauthors). [arXiv:2403.01651]
- Gray-categories model algebraic tricategories. Theory Appl. Categ. [arXiv:2203.03748]
- OSU REU project: Classifying module categories for generalized Temperley-Lieb-Jones $*$-2-categories. (with a coauthor). Internat. J. Math. [DOI:10.1142/S0129167X20500275, arXiv:1905.00471]
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Daniel WALLICK
- An operator algebraic approach to symmetry defects and fractionalization. (with coauthors) [arXiv:2410.23380]
- Superselection sectors for posets of von Neumann algebras. (with coauthors). [arXiv:2410.21454]
- Local topological order and boundary algebras (with coauthors). To appear Forum of Math. Sigma. [arXiv:2307.12552]
- Boundary algebras of the Kitaev Quantum Double model. (with coauthors). J. Math. Phys. [arXiv:2309.13440 DOI:10.1063/5.0212164]
- An algebraic quantum field theoretic approach to toric code with gapped boundary J. Math. Phys. [DOI:10.1063/5.0149891, arXiv:2212.01952]
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Brett HUNGAR
- Manifestly unitary higher Hilbert spaces (with coauthors). [arXiv:2410.05120]
- Dagger n-categories (with coauthors). [arXiv:2403.01651]
- Boundary algebras of the Kitaev Quantum Double model. (with coauthors). J. Math. Phys. [arXiv:2309.13440]
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Anupama BHARDWAJ
- Superselection sectors for posets of von Neumann algebras. (with coauthors) [arXiv:2410.21454]
- Chumeng DI
- Greyson WESLEY
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Quan CHEN
- thesis: Higher symmetries in operator algebras
- 2023-26: postdoc at Vanderbilt University with Dietmar BISCH
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Zachary DELL
- thesis: Characterization of unitary braided-enriched monoidal categories
- 2022-: ESports Rocket League coach at Illinois State University
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Peter HUSTON
- thesis: Tensor category constructions in topological phases of matter
- 2022-25: postdoc at Vanderbilt University with Dietmar BISCH
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Roberto HERNANDEZ PALOMARES
- thesis: Quantum symmetries for quantum spaces
- 2021-22: postdoc at Texas A&M working with Eric ROWELL
- 2023-25: postdoc at Waterloo working with Michael BRANNAN and Matthew KENNEDY
- Corey JONES, now tenure track assistant professor at North Carolina State University
Mathematics Teaching
- MATH 6211 Real Analysis: Autumn 2019, Autumn 2020, Autumn 2024
- MATH 7211 and 7212 Functional Analysis: Autumn 2017 and Spring 2018, Spring 2022, Spring 2024
- MATH 8110 Higher Linear Algebra: Autumn 2023
- MATH 8800 Topological Phases of Matter: Spring 2021
- MATH 2568 Linear Algebra: Spring 2019, Autumn 2019
- MATH 8160 Quantum Algebra: Autumn 2018 course notes
- MATH 3345 Foundations of Higher Mathematics: Autumn 2016
Mathematics Research
Peer reviewed journal articles
Peer reviewed journal articles
- Corey Jones, Pieter Naaijkens, David Penneys, and Daniel Wallick. Local topological order and boundary algebras. 2023. To appear Forum of Math. Sigma. [arXiv:2307.12552]
- Cain Edie-Michell, Masaki Izumi, and David Penneys Classification of Z/2Z-quadratic unitary fusion categories. 2021. To appear Quantum Topol. [arXiv:2108.01564, DOI:10.4171/QT/201]
- Zachary Dell, Peter Huston, and David Penneys. Unitary braided-enriched monoidal categories. Quantum Topol. 15 (2024), no. 3, 567--632. [arXiv:2208.14992, DOI:10.4171/QT/226]
- Chian Yeong Chuah, Brett Hungar, Kyle Kawagoe, David Penneys, Mario Tomba, Daniel Wallick, and Shuqi Wei. Boundary algebras of the Kitaev Quantum Double model. J. Math. Phys. 65 (2024), no. 10, Paper No. 102201. [arXiv:2309.13440 DOI:10.1063/5.0212164]
- Kyle Kawagoe, Corey Jones, Sean Sanford, David Green, and David Penneys. Levin-Wen is a gauge theory: entanglement from topology. Comm. Math. Phys. 405 (2024), no. 11, Paper No. 266. [arXiv:2401.13838, DOI:10.1007/s00220-024-05144-x]
- Quan Chen, Corey Jones, and David Penneys. A categorical Connes' \chi(M). Math. Ann. 389 (2024), no. 3, 2051--2121. [arXiv:2111.06378, DOI:10.1007/s00208-023-02695-7]
- André Henriques, David Penneys, and James Tener. Unitary anchored planar algebras. Comm. Math. Phys. 405 (2024), no. 6, Paper No. 137 [arXiv:2301.11114 DOI:10.1007/s00220-024-04985-w]
- David Green, Peter Huston, Kyle Kawagoe, David Penneys, Anup Poudel, and Sean Sanford. Enriched string-net models and their excitations. Quantum 8, 1301 (2024) [arXiv:2305.14068]
- Jessica Christian, David Green, Peter Huston, and David Penneys. A lattice model for condensation in Levin-Wen systems. J. High Energy Phys. (2023), no.9, Paper No. 55, 55 pp. [arXiv:2303.04711 DOI:10.1007/JHEP09(2023)055]
- Peter Huston, Fiona Burnell, Corey Jones, and David Penneys. Composing topological domain walls and anyon mobility. SciPost Phys. 15, 076 (2023). [arXiv:2208.14018, DOI:10.21468/SciPostPhys.15.3.076]
- Pinhas Grossman, Scott Morrison, David Penneys, Emily Peters, and Noah Snyder. The Extended Haagerup fusion categories. Ann. Sci. Éc. Norm. Supér. (4) 56 (2023), no. 2, 589–664. [arXiv:1810.06076, DOI:10.24033/asens.2541]
- André Henriques and David Penneys. Representations of fusion categories and their commutants. Selecta Math. (NS) 29 (2023), no. 3, Paper No. 38. [arXiv:2004.08271, DOI:10.1007/s00029-023-00841-2]
- Narjess Afzaly, Scott Morrison, and David Penneys. The Classification of Subfactors with Index at Most 5+1/4. Mem. Amer. Math. Soc. 284 (2023), no. 1405, ISBN: 978-1-4704-4712-0 [arXiv:1509.00038, DOI:10.1090/memo/1405]
- Corey Jones, David Penneys, and David Reutter. A 3-categorical perspective on G-crossed braided categories. J. Lond. Math. Soc. (2) 107 (2023), no. 1, 333–406. [arXiv:2009.00405, DOI:10.1112/jlms.12687]
- André Henriques, David Penneys, and James Tener. Planar Algebras in Braided Tensor Categories. Mem. Amer. Math. Soc. 282 (2023), no. 1392, ISBN: 978-1-4704-5540-8 [arXiv:1607.06041, DOI:10.1090/memo/1392]
- Konrad Aguilar, Michael Hartglass, and David Penneys. Compact quantum metric spaces from free graph algebras. Internat. J. Math. 33 (2022), no. 10-11, 2250073, 23 pp. [arXiv:2109.06985, DOI:10.1142/S0129167X22500732]
- Corey Jones, Scott Morrison, David Penneys, and Julia Plavnik. Extension theory for braided-enriched fusion categories. Int. Math. Res. Not. IMRN 2022, no. 20, 15632--15683 [arXiv:1910.03178, DOI:10.1093/imrn/rnab133]
- Quan Chen, Roberto Hernández Palomares, Corey Jones, and David Penneys. Q-system completion for C* 2-categories. J. Funct. Anal. 283 (2022), no. 3, Paper No. 109524 [arXiv:2105.12010, DOI:10.1016/j.jfa.2022.109524]
- Quan Chen and David Penneys. Q-system completion is a 3-functor. Theor. Appl. Categ. Vol. 38, 2022, No. 4, 101-134 [arXiv:2106.12437, published article available here]
- Desmond Coles, Peter Huston, David Penneys, and Srivatsa Srinivas. The module embedding theorem via towers of algebras. J. Funct. Anal. 280 (2021), no. 11., Paper No. 108965 [arXiv:1810.07049, DOI:10.1016/j.jfa.2021.108965]
- David Penneys. Unitary dual functors for unitary multitensor categories. Higher Structures 4(2):22-56, 2020. [arXiv:1808.00323, DOI:10.21136/HS.2020.09, more details for Lemma 3.26]
- Scott Morrison and David Penneys. Monoidal categories enriched in braided monoidal categories. Int. Math. Res. Not. 2019, no. 11, 3527--3579 [arXiv:1701.00567, DOI:10.1093/imrn/rnx217]
- Corey Jones and David Penneys. Realizations of algebra objects and discrete subfactors. Adv. Math. 350 (2019), p 588-661 [arXiv:1704.02035, DOI:10.1016/j.aim.2019.04.039]
- Marcel Bischoff, Corey Jones, Yuan-Ming Lu, and David Penneys. Spontaneous symmetry breaking from anyon condensation. J. High Energ. Phys. (2019) 2019: 62. [arXiv:1811.00434, DOI:10.1007/JHEP02(2019)062]
- Corey Jones and David Penneys. Operator algebras in rigid C*-tensor categories. Comm. Math. Phys. 355 (2017), no. 3, 1121--1188. [arXiv:1611.04620, DOI:10.1007/s00220-017-2964-0]
- André Henriques and David Penneys. Bicommutant categories from fusion categories. Selecta Math. (NS) 23 (2017), no. 3, 1669--1708. [arXiv:1511.05226, DOI:10.1007/s00029-016-0251-0]
- Michael Hartglass and David Penneys. C*-algebras from planar algebras I: canonical C*-algebras associated to a planar algebra. Trans. Amer. Math. Soc. 369 (2017), no. 6, 3977--4019. [arXiv:1401.2485, DOI:10.1090/tran/6781]
- André Henriques, David Penneys, and James Tener. Categorified trace for module tensor categories over braided tensor categories. Documenta Math. 21 (2016) 1089--1149 [arXiv:1509.02937, published article available here]
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Masaki Izumi, Scott Morrison, and David Penneys.
Quotients of A_2*T_2.
Canad. J. Math.
68 (2016), no. 5, 999--1022.
[DOI:10.4153/CJM-2015-017-4]
(This is an abridged version of the arXiv preprint Fusion categories between C \boxtimes D and C * D. [arXiv:1308.5723]) - David Penneys and Emily Peters. Calculating two-strand jellyfish relations. Pacific J. Math. 277 (2015), no. 2, 463-510. [arXiv:1308.5197, DOI:10.2140/pjm.2015.277-2]
- Scott Morrison and David Penneys. 2-supertransitive subfactors at index 3+\sqrt{5} J. Funct. Anal. 269 (2015), no. 9, 2845-2870. [arXiv:1406.3401, DOI:10.1016/j.jfa.2015.06.023]
- Vaughan F. R. Jones and David Penneys. Infinite index subfactors and the GICAR categories. Comm. Math. Phys. 339 (2015), no. 2, 729-768. [arXiv:1410.0856, DOI:10.1007/s00220-015-2407-8, corrected proof of Lemma 5.2]
- Masaki Izumi, Scott Morrison, David Penneys, Emily Peters, and Noah Snyder. Subfactors of index exactly 5. B. Lond. Math. Soc. (2015) 47 (2): 257-269. [arXiv:1406.2389, DOI:10.1112/blms/bdu113]
- Scott Morrison and David Penneys. Constructing spoke subfactors using the jellyfish algorithm. Trans. Amer. Math. Soc. 367 (2015), no. 5, 3257-3298. [arXiv:1208.3637, DOI:10.1090/S0002-9947-2014-06109-6]
- David Penneys. Chirality and principal graph obstructions. Adv. Math. 273(19):32-55, 2015. [arXiv:1307.5890, DOI:10.1016/j.aim.2014.11.021]
- Zhengwei Liu, Scott Morrison, and David Penneys. 1-supertransitive subfactors with index at most 6+1/5. Comm. Math. Phys. 334 (2015), no. 2, 889-922. [arXiv:1310.8566, DOI:10.1007/s00220-014-2160-4]
- Michael Hartglass and David Penneys. C*-algebras from planar algebras II: the Guionnet-Jones-Shlyakhtenko C*-algebras. J. Funct. Anal. 267 (2014), no. 10, 3859--3893. [arXiv:1401.2486, DOI:10.1016/j.jfa.2014.08.024]
- Stephen Bigelow and David Penneys. Principal graph stability and the jellyfish algorithm. Math. Ann. 358 (2014), no. 1-2, 1-24. [arXiv:1208.1564, DOI:10.1007/s00208-013-0941-2]
- David Penneys. A planar calculus for infinite index subfactors. Comm. Math. Phys. 319 (2013), no. 3, 595-648. [arXiv:1110.3504, DOI:10.1007/s00220-012-1627-4]
- Arnaud Brothier, Michael Hartglass, and David Penneys. Rigid C*-tensor categories of bimodules over interpolated free group factors. J. Math. Phys. 53 (2012), no. 12, 123525 (43 pages), [arXiv:1208.5505, DOI:10.1063/1.4769178]
- David Penneys and James Tener. Subfactors of index less than 5, part 4: vines. Internat. J. Math. 23 (2012), no. 3, 1250017 (18 pages) [arXiv:1010.3797, DOI:10.1142/S0129167X11007641]
- Scott Morrison, David Penneys, Emily Peters, and Noah Snyder. Subfactors of index less than 5, part 2: triple points. Internat. J. Math. 23 (2012), no. 3, 1250016 (33 pages) [arXiv:1007.2240, DOI:10.1142/S0129167X11007586]
- David Penneys, A cyclic approach to the annular Temperley-Lieb category. J. Knot Theory and its Ramifications 21 (2012), no. 6, 1250049 (40 pages) [arXiv:0912.1320, DOI:10.1142/S0218216511010012]
- Vaughan F. R. Jones and David Penneys. The embedding theorem for finite depth subfactor planar algebras. Quantum Topol. 2 (2011), 301-337 [arXiv:1007.3173, DOI:10.4171/QT/23]
- Corey Jones and David Penneys. Q-systems and compact W*-algebra objects. Topological phases of matter and quantum computation, 63--88, Contemp. Math., 747, Amer. Math. Soc., Providence, RI, 2020. [arXiv:1707.02155, DOI:10.1090/conm/747/15039]
- Zhengwei Liu, Scott Morrison, and David Penneys. Lifting shadings on symmetrically self-dual subfactor planar algebras. Topological phases of matter and quantum computation, 51--61, Contemp. Math., 747, Amer. Math. Soc., Providence, RI, 2020. [arXiv:1709.05023, DOI:10.1090/conm/747/15038]
- Zhengwei Liu and David Penneys. The generator conjecture for $3^G$ subfactor planar algebras. Proceedings of the 2014 Maui and 2015 Qinhuangdao conferences in honour of Vaughan F. R. Jones' 60th birthday, 344--366, Proc. Centre Math. Appl. Austral. Nat. Univ., 46, Austral. Nat. Univ., Canberra, 2017. [arXiv:1507.04794, available online here]
- David Penneys (joint work with Marcel Bischoff, Ian Charlesworth, Samuel Evington, Luca Giorgetti, and André Henriques). Modular distortion for II_1 multifactor bimodules. 2020. To appear Oberwolfach Reports. [PDF]
- David Penneys (joint work with André Henriques and James Tener). Planar algebras in modular tensor categories. 2015. Oberwolfach Reports. [DOI:10.4171/OWR/2015/16, PDF]
- Scott Morrison, David Penneys, and Julia Plavnik. Completion for braided enriched monoidal categories. 2018. [arXiv:1809.09782]
- Marcel Bischoff, Ian Charlesworth, Samuel Evington, Luca Giorgetti, and David Penneys. Distortion for multifactor bimodules and representations of multifusion categories. 2020. [arXiv:2010.01067]
- André Henriques, David Penneys, and James Tener. Classification of finite depth objects in bicommutant categories via anchored planar algebras. 2023. [arXiv:2307.13822]
- Giovanni Ferrer, Brett Hungar, Theo Johnson-Freyd, Cameron Krulewski, Lukas Muller, Nivedita, David Penneys, David Reutter, Claudia Scheimbauer, Luuk Stehouwer, and Chetan Vuppulury. Dagger n-categories. 2024. [arXiv:2403.01651]
- Quan Chen, Giovanni Ferrer, Brett Hungar, David Penneys, and Sean Sanford. Manifestly unitary higher Hilbert spaces. 2024. [arXiv:2410.05120]
- Anupama Bhardwaj, Tristan Brisky, Chian Yeong Chuah, Kyle Kawagoe, Joseph Keslin, David Penneys, and Daniel Wallick. Superselection sectors for posets of von Neumann algebras. 2024. [arXiv:2410.21454]
- André Henriques, Nivedita, and David Penneys. Complete W*-categories 2024. [arXiv:2411.01678]
- Thibault D. Décoppet, Peter Huston, Theo Johnson-Freyd, Dmitri Nikshych, David Penneys, Julia Plavnik, David Reutter, and Matthew Yu. The classification of fusion 2-categories 2024. [arXiv:2411.05907]
- Pavel Etingof and David Penneys. Rigidity of non-negligible objects of moderate growth in braided categories 2024. [arXiv:2412.17681]
- David Penneys. Planar structure for inclusions of finite von Neumann algebras. 2012. [pdf]
Conference and seminar talks
2025
2025
- Great Lakes Mathematical Physics Meeting at University of Kentucky 6/6-8. TBD
- Generalized Symmetries: High-Energy, Condensed Matter and Mathematics at KITP 4/7-11. TBD
- UC Santa Barbara 4/1. Topology Seminar. TBD
- Yale University 3/5. Graduate Theory Seminar (Physics Department). Local topological quantum codes and topological holography
- ECOAS at NCSU 11/9-10. Superselection sectors for posets of von Neumann algebras
- Vanderbilt University 9/13. Subfactor seminar. Subfactor techniques in topological order
- Vanderbilt University 9/12. Colloquium. Local Topological Quantum Codes
- SLMath Quantum Symmetries Reunion 7/15. Seminar talk -- 3Hilb
- SLMath Quantum Symmetries Reunion 7/15. Lightning talk -- Boundary algebras for enriched Levin-Wen models
- ICMS workshop on Categorical symmetries in Quantum Field Theory 10/9-13. Levin-Wen is a gauge theory.
- North Carolina State University 3/28. Corey Jones' research group seminar. What is the toric code?
- UCSD Functional Analysis Seminar 10/17. An operator algebraic axiomatization of local topological order.
- ICMS workshop on Topological Quantum Computation 10/9-13. Local topological order and boundary algebras. [video]
- Purdue Operator Algebras Seminar 9/12. An operator algebraic axiomatization of local topological order.
- Yasu Festa 60 7/24-28. Local topological order and boundary algebras. [video]
- Purdue University 6/17. GOALS culminating workshop What is topological order?
- Zoom workshop Dagger higher categories 6/12. Some subtleties about unitary multitensor categories
- UM Dearborn 5/25. REU speaker. What is topological order?
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Vanderbilt NCGOA on von Neumann algebras 5/8-11. Local topological order and boundary algebras.[Unable to attend; talk given by Daniel Wallick]
- Dalhousie University 12/1. Colloquium. Higher linear algebra and topological order
- Tsinghua University, 11/8. Quantum Symmetry Seminar. A 3-categorical perspective on G-crossed braided categories
- Hausdorff Research Institute for Mathematics 8/30. Follow-up Workshop to TP "Von Neumann Algebras". A categorical Connes' \chi(M)
- Harvard University 6/19-23. New Frontiers: Interactions between Quantum Physics and Mathematics, Composing topological domain walls and anyon mobility. [Beamer slides]
- Concentration Week on Quantum Groups, Tensor Categories, and Subfactors, 5/24-28. Introduction to the classification program for subfactors. [course notes for first two talks, Beamer slides for third talk]
- AMS Joint Meetings 4/6. Special Session on fusion categories and their applications in physics. Classification of Z/2Z-quadratic unitary fusion categories. [synoptic chart, Beamer slides]
- Cardiff Virtual GAPT Seminar 12/2. Fusion categories in mathematics and physics
- George Washington University 11/12. Colloquium. Fusion categories and quantum symmetry
- AMS Fall Western Sectional Meeting 10/23-4. Special Session on tensor categories and applications. Classification of Z/2Z-quadratic unitary fusion categories
- Michigan State University 10/8. Colloquium. Fusion categories in mathematics and physics
- Indiana University 10/1. Colloquium. Fusion categories and some applications in mathematics and physics
- BIRS/IASM workshop 9/20-24 on Subfactors, Vertex Operator Algebras, and Tensor Categories. A categorical Connes' $\chi(M)$ [notes]
- Great Plains Operator Theory Symposium, 5/10. C*-algebras, right correspondences, and Q-systems, part I: What is a Q-system? [Beamer slides]
- Vanderbilt Subfactor Seminar, 4/30. Classifying small index subfactors
- UCLA Functional Analysis Seminar, 4/14. The classification of standard invariants of index at most 5.25 [Beamer slides]
- Brazos Analysis Seminar, 3/21. Q-system completion for C* 2-categories [Beamer slides]
- Quantum Groups Seminar, 1/11. Discrete subfactors, realization of algebra objects, and Q-system completion [Beamer slides]
- AMS JMM Special Session on Advances in Operator Algebras, 1/7. Distortion for multifactor bimodules and representations of multifusion categories. [Beamer slides]
- MSRI Connections for Women: Quantum Symmetries, 1/23-24. Open problems on subfactors and unitary tensor categories
- Oberwolfach workshop on Subfactors and their applications 10/28-11/1 Modular distortion for II_1 multifactor bimodules
- University of Virginia 9/10. Distortion for II_1 multifactor bimodules
- Vanderbilt NCGOA 5/3-9. G-graded extensions of braided enriched fusion categories
- AMS Joint Meetings 1/16. Special Session on Hopf algebras and tensor categories. The module embedding theorem. [Beamer slides]
- UCLA 11/15. Functional analysis seminar. The maximal atlas of the Extended Haagerup subfactor
- GPOTS, Miami University (Ohio) 5/29-6/2. Plenary speaker. The maximal atlas of the extended Haagerup subfactor planar algebra
- University of Delaware 3/23. Analysis Seminar. Classifying small quantum symmetries
- Santa Clara University 3/13. Colloquium. Planar algebras and evaluation algorithms
- UC Berkeley 3/12. Probabilistic Operator Algebras Seminar. Standard invariants for discrete subfactors
- Texas A&M 1/30. Linear Analysis Seminar. Standard invariants for discrete subfactors
- Texas A&M 1/30. Algebra Seminar. Exotic fusion categories: EH3 exists!
- George Washington University 11/13. Topology Seminar. Monoidal categories enriched in braided monoidal categories
- UM Dearborn 4/29. Analysis Day. Realizations of algebra objects and discrete subfactors
- STEAM Factory, OSU 4/20. April STEAM Exchange - Weeds. [Beamer slides (with pauses)]
- Purdue University 4/13. Operator algebras seminar. Realizations of algebra objects and discrete subfactors
- AMS Sectional Meeting 4/1-2. Special Session on Fusion categories and applications. Commutants of multifusion categories [Beamer slides]
- Ohio University 3/30. Colloquium. Classifying small quantum symmetries
- Australian National University 3/24. Quantum mathematics meeting. Enriched operator algebras
- Australian National University 3/21. Algebra and topology seminar. Operator algebras in rigid C*-tensor categories
- Vanderbilt University 2/24. Subfactor seminar. Operator algebras in rigid C*-tensor categories
- Isaac Newton Institute, Cambridge, England 1/23-27. Structure of Operator Algebras: Subfactors and Fusion Categories. Operator algebras in rigid C*-tensor categories, part II
- Isaac Newton Institute, Cambridge, England 1/11, 12, 13, 16. Operator Algebras: Subfactors and their Applications. Mini-course on Introduction to subfactor theory. [course notes (incomplete first draft, posted 2017/2/17)]
- AMS Joint Meetings 1/6-9. Special Session on Fusion Categories and Quantum Symmetries. Tensor categories enriched in braided tensor categories [Beamer slides]
- Workshop on Subfactor Theory, Quantum Field Theory, and Quantum Information at Harvard University 10/8-10. Enriched quantum symmetry
- Wabash conference in modern analysis at IUPUI 9/17-18. Bicommutant categories from (multi)fusion categories
- Hausdorff Research Institute for Mathematics (HIM), Bonn, Germany 7/4-8. Workshop on von Neumann algebras. Bicommutant categories from (multi)fusion categories
- AMS Special Session on Fusion Categories and Topological Phases of Matter 4/10. Categorified trace for module tensor categories over braided tensor categories [Beamer slides]
- Vanderbilt University 4/8. Subfactor seminar. Bicommutant categories from (multi)fusion categories
- Ohio State University 2/8. Colloquium. Classifying small quantum symmetries
- Pennsylvania State University 1/28. Noncommutative geometry seminar. Subfactors and NCG
- Pennsylvania State University 1/27. Lunchtime geometry seminar. Classifying small quantum symmetries
- AMS Joint Meetings 1/6-9. Special Session on Classification problems in operator algebras. Bicommutant categories [Beamer slides]
- University of Virginia 12/7. Colloquium. Classifying quantum symmetries
- UC Santa Barbara 11/10. Topology seminar. Planar algebras in modular tensor categories
- North Carolina State University 10/21. Geometry and topology seminar. Planar algebras in modular tensor categories
- North Carolina State University 10/19. Algebra and combinatorics seminar. Classifying small quantum symmetries
- Stanford University 7/28. Planar algebras
- International Conference on subfactor theory in mathematics and physics, - in honor of Vaughan Jones' 60th Birthday, Qinhuangdao, China, 6/29-7/3. Subfactors: past, present, and future [Beamer slides]
- University of Kyoto 7/7. Operator algebra seminar. Bicommutant categories
- International Conference on C*-algebras and Dynamical Systems, - in honor of George Elliott's 70th Birthday, Shijiazhuang, China, 6/29-7/3. C*-algebras from planar algebras [Beamer slides]
- GPOTS, Purdue University 5/26-30. Half hour plenary speaker. The 2D2 subfactor. [Beamer slides]
- USC Hopf algebras and tensor categories mini-meeting 5/21-22. Planar algebras in modular tensor categories
- Bodega Bay Subfactor Microconference 5/16-17. Self duality.
- UC Berkeley 5/8-11. Extended Probabilistic Operator Algebra Seminar. Classifying small index subfactors [Beamer slides]
- Oberwolfach meeting on Subfactors and Conformal Field Theory 3/28. Planar algebras in modular tensor categories
- Caltech Noncommutative geometry seminar 3/4. Subfactors and NCG
- AMS Joint Meetings, Special Session on Quantum Information and Fusion Categories (a Mathematical Research Communities session), San Antonio 1/11. Classifying small index subfactors [Beamer slides]
- UC San Diego 12/4. The 2D2 subfactor
- UC Davis Mathematical Physics & Probability seminar 10/29. Applications of subfactors and fusion categories to mathematical physics [Beamer slides]
- USC Hopf working seminar 10/14. Planar algebras, Hopf algebras, and fusion categories
- UCLA Workshop on von Neumann algebras and ergodic theory 9/22-26. Classifying small index subfactors, [Beamer slides]
- Stanford University 8/22. Planar algebras and evaluation algorithms
- AMS MRC on Mathematics of Quantum Phases of Matter and Quantum Information 6/24-30. Ostrik's classification of rank 3 pivotal fusion categories
- GPOTS, Kansas State University 5/27-31. Half hour plenary speaker. Classifying small index subfactors [Beamer slides]
- Vanderbilt NCGOA 5/2-8. Mini course on Introduction to subfactors. [course notes (first draft), written notes used during lecture, notes on other talks]
- Vanderbilt 4/25. Classifying small index subfactors [notes]
- Duke University 4/8. Planar algebras and evaluation algorithms
- NC State University 4/7. Planar algebras and evaluation algorithms
- University of New South Wales 3/17. 1-supertransitive subfactors with index at most 6.2
- The Australian National University 3/11. 1-supertransitive subfactors with index at most 6.2 [notes]
- UC Riverside 2/27 (Colloquium). Classifying small index subfactors [Beamer slides]
- UC Davis 1/6. Exotic fusion categories
- UC Berkeley 11/8. Free graph algebras and GJS C*-algebras
- UC San Diego 11/7. 1-supertransitive subfactors with index at most 6.2
- Subfactors in Maui 7/15. Chirality and principal graph obstructions
- Canadian Annual Symposium on Operator Algebras and Their Applications (COSy) 5/27. Subfactors of index 3+\sqrt{5} [Beamer slides]
- Institut de Mathematiques de Bourgogne - workshop on fusion categories 5/21-3. Fusion categories between C \boxtimes D and C * D (with applications to subfactors at index 3+\sqrt{5}) [Beamer slides]
- Northwestern University 4/24. Subfactors of index 3+\sqrt{5}
- Loyola University 4/17. Planar algebras
- University of Waterloo 4/5. GJS C*-algebras
- University of Tokyo 3/12. Constructing subfactors with jellyfish
- The Australian National University 2/5. Planar algebra
- Western University 12/10. Constructing subfactors with jellyfish
- Univrtsity of Michigan, Dearborn colloquium 12/7. Planar algebra
- UC San Diego 11/13. Constructing subfactors with jellyfish
- UC Santa Barbara 11/13. Constructing subfactors with jellyfish
- ECOAS 10/7. Constructing subfactors with the jellyfish algorithm [Beamer slides]
- Subfactors in Maui 7/16. Spokes, jellyfish, trains, and tails
- UCLA 6/6. Jellyfish, trains, and principal graph stability
- UC Santa Barbara 1/31. Automated jellyfish
- Purude ECOAS 10/15. Infinite index subfactors and the GICAR algebras [Beamer slides]
- Subfactors in Maui 7/18. Infinite index
- AMS Joint Meetings, New Orleans 1/8. Eliminating weeds and vines in the classification of subfactors to index 5 [Beamer slides]
- University of Tokyo operator algebras seminar 7/8. Killing weeds with annular multiplicities *10
- Kyushu University operator algebras seminar 7/26. Killing weeds with annular multiplicities *10
- Vanderbilt NCGOA 5/11. The embedding theorem for finite depth subfactor planar algebras [Beamer slides]
- IMSC colloquium 2/26. Categories and pictures
- GWU topology seminar 1/12. Examples of planar algebras
- GWU analysis seminar 3/25. Planar algebras and knot polynomials
Conferences and seminars organized
International and national conferences
International and national conferences
- Terry Gannon, Theo Johnson-Freyd, Julia Plavnik, and I are organizing the BIRS workshop Subfactors and Fusion (2-)Categories, December 4-8, 2023.
- Kristin Courtney, Andre Henriques, Emily Peters, Aaron Tikuisis, Stuart White, and I are organizing a twinned workshop on Actions of Tensor Categories on C*-algebras November 6-10, 2023 at ICMS and the Fields Institute
- Theo Johnson-Freyd and I are organizing an online Zoom workshop on Dagger higher categories June 12-15, 2023.
- Ovidiu Costin, Rodica Costin, Jan Lang, and I hosted the Great Plains Operator Theory Symposium May 15-19, 2023 at OSU.
- Jacob Bridgeman, Tobias Osbourne, Julia Plavnik, and I are organizing the AIM workshop Higher Categories and Topological Order, September 26-30, 2022.
- Jacob Bridgeman, Tobias Osbourne, Julia Plavnik, and I organized the AIM workshop Fusion Categories and Tensor Networks, March 8-12, 2021.
- Emily Peters, Aaron Tikuisis, Stuart White, and I are organizing a workshop at IPAM on Actions of tensor categories on C*-algebras, January 25-29, 2021.
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Ezekiel Johnston-Halperin, Roland Kawakami, Ronald Reano and I are organizing a Quantum Information Science and Technology session at OSU's Materials Week 2020 - Corey Jones, Henri Moscovici, and I will host the Seventeenth East Coast Operator Algebra Symposium October 12-13, 2019 at The Ohio State University.
- Corey Jones and I are organizing the Summer Research Program on Quantum Symmetries June 3-14, 2019 at The Ohio State University.
- Maria Angelica Cueto, Krystal Taylor, Dan Thompson, and I are organizing a Graduate Advising Workshop at The Ohio State University June 1-2, 2019. [Dan Thompson's article in the AMS Notices]
- Contact organizer for a workshop on Fusion Categories and Subfactors at BIRS 2018/10/14-19 (organized with Gannon, Morrison, and Plavnik)
- Lead for an American Mathematical Society Mathematics Research Communities workshop on Quantum symmetries: subfactors and fusion categories, June 10-16, 2018 (organized with Julia Plavnik and Noah Snyder with assistants Paul Bruillard and Corey Jones)
- Contact organizer for a Special Session on Quantum Symmetries at the AMS Central Spring Sectional Meeting at The Ohio State University, March 17-18, 2018 (organized with Julia Plavnik)
- Contact organizer for Quantum Symmetries: Subfactors and Planar Algebras July 17-21, 2017, Maui, Hawaii (organized with Dietmar Bisch, Arnaud Brothier, Vaughan Jones, Scott Morrison, Noah Snyder, James Tener and Rufus Willet)
- Contact organizer for a Special Session on von Neumann algebras and their applications at the 2017 Mathematical Congress of the Americas (organized with Dietmar Bisch, Román Sasyk, and Thomas Sinclair)
- Organizer for an AMS Special Session on Advances in operator algebras at the Joint Meetings in Atlanta 2017/1/4-7 (organized with Michael Hartglass and Elizabeth Gillaspy)
- Contact organizer for an AIM SQuaREs workshop 2016/9/12-16 (consisting of Grossman, Izumi, Morrison, Penneys, Peters, and Snyder)
- Contact organizer for an AMS Special Session on von Neumann algebras at the AMS Sectional Meeting in Memphis 2015/10/17-8 (organized with Vaughan F. R. Jones)
- Wrote a proposal for the workshop Subfactors and Conformal Field Theory at Oberwolfach 2015/03/22-8 with the official organizers (Bisch, Gannon, Jones, and Kawahigashi)
- Contact organizer for an AMS Special Session on Classification problems in operator algebras at the Joint Meetings in San Antonio 2015/1/11-12 (organized with Arnaud Brothier, Ionut Chifan, Darren Creutz, and Remus Nicoara)
- Co-organizer for Subfactor Theory in Mathematics and Physics, in honor of the 60th birthday of Vaughan Jones 2014/7/14-18 (organized with Bisch, Brothier, Jones, Morrison, Snyder, Tener, and Willet). Conference proceedings available online here.
- Contact organizer for a workshop on Subfactors and fusion categories at BIRS 2014/4/13-8 (organized with Jones, Morrison, Peters, and Snyder)
- Contact organizer for an AMS Special Session on Classification problems in operator algebras at the Joint Meetings in Baltimore 2014/1/15-6 (organized with Ionut Chifan)
- Contact organizer for Subfactors in Maui 2011
- Contact organizer for Subfactors in Tahoe 2011
- Contact organizer for Subfactors in Tahoe 2010
- The annual Operators on Hilbert spaces In Ohio conference. This year's conference is on 2018/4/28.
- Bodega Bay Subfactor Microconference 2016 5/16-17.
- UC Subfactor retreat 2015 at UC Santa Barbara 11/9-12.
- Bodega Bay Subfactor Microconference 2015 5/16-17.
- Quantum algebra seminar at the Fields Institute Fall 2013 - Spring 2014 [talk abstracts]
- Subfactor seminar at UC Berkeley Fall 2009 - Spring 2012
- Student subfactor seminar at UC Berkeley Spring 2008 - Fall 2009
Surveys, expository articles, and miscellaneous
- Here is a video of the synoptic chart of tensor categories animated by undergraduate researcher Quinn Kolt in Spring 2022.
- AMS memorial article for Vaughan F. R. Jones
- Handouts on introductory subfactor theory:
- A terse note on algebras, module categories, and planar algebras
- A proof of a generalized Ocneanu compactness theorem
- Notes from the AIM workshop on classifying fusion categories
- Categorified Morita equivalence
- Noah Snyder's talk on subfactors and tensor categories at the 2010 Subfactors in Tahoe retreat
- A subfactor planar algebra everyone will understand
- A homework problem from Peter Teichner's homological algebra class about Temperley-Lieb diagrams and 2-categories
- Cyclic homology
- Notes on linear algebra that I wrote Summer 2008 [pdf]
- Qualifying exam syllabus. Passed on August 15, 2007.
- Rules for quanum go fish, a fun game to play.
last modified: 2025/1/23