David Penneys
Professor of Mathematics at The Ohio State University
Office: Room 752 Math Tower
Email: penneys (dot) 2 (at) osu (dot) edu

dsp in la

About me:

I received my Ph.D. from the University of California, Berkeley in 2012 studying subfactor theory 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 quantum symmetries via operator algebras and tensor categories with applications to quantum many-body systems, especially topologically ordered phases of matter. In nature and the physical sciences, symmetry is described by group actions, where an object X has G-symmetry if G is a collection of self-maps closed under composition and inversion. Typically these self maps are morphisms in some category, such as topological spaces, vector spaces, or algebras, and G acts via a map to End(X). Quantum mathematical objects naturally live in higher categories, where the collections of self-maps End(X) form higher monoidal categories. Thus higher groups and higher monoidal categories act on X via monoidal functors to End(X), allowing for richer non-invertible/categorical/quantum symmetries.

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.

Here is a link to a book in progress with Giovanni Ferrer and Kyle Kawagoe called Unitary Quantum Symmetries Lite.


Graduate students and postdocs

Current graduate students and their dissertation work Current postdocs Former PhD students Former postdocs
  • Corey JONES, now tenure track assistant professor at North Carolina State University


Mathematics Teaching


Mathematics Research

Peer reviewed journal articles
  • 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. To appear Comm. Math. Phys. [arXiv:2410.21454]
  • Marcel Bischoff, Ian Charlesworth, Samuel Evington, Luca Giorgetti, and David Penneys. Distortion for multifactor bimodules and representations of multifusion categories. 2020. To appear Documenta Math. [arXiv:2010.01067]
  • 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]
  • 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]
Peer reviewed conference proceedings
  • 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]
Additional conference proceedings
  • 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]
arXiv preprints
  • Scott Morrison, David Penneys, and Julia Plavnik. Completion for braided enriched monoidal categories. 2018. [arXiv:1809.09782]
  • 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]
  • 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]
Dissertation
  • David Penneys. Planar structure for inclusions of finite von Neumann algebras. 2012. [pdf]


Conference and seminar talks

2025 2024
  • 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?
2023
  • 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?
  • Vanderbilt NCGOA on von Neumann algebras 5/8-11. Local topological order and boundary algebras. [Unable to attend; talk given by Daniel Wallick]
2022 2021 2020 2019
  • 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]
2018
  • 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!
2017 2016 2015 2014
  • 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
2013
  • 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
2012
  • 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
2011
  • 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]
2010
  • 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]
2009
  • IMSC colloquium 2/26. Categories and pictures
  • GWU topology seminar 1/12. Examples of planar algebras
2008
  • GWU analysis seminar 3/25. Planar algebras and knot polynomials
Here is a pdf file of all abstracts of conference and seminar talks I have given from 2007-present.


Conferences and seminars organized


International and national conferences Microconferences Seminars
  • 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


last modified: 2025/4/24