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


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 20122014 at the University of Toronto under the supervision of Dror BarNatan and George Elliott.
From 20142016, 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 noncommutative 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.
Mathematics Teaching
Mathematics Research
Peer reviewed journal articles

Marcel Bischoff, Corey Jones, YuanMing Lu, and David Penneys.
Spontaneous symmetry breaking from anyon condensation.
To appear J. High Energy Phys.
[DOI:10.1007/JHEP02(2019)062,
arXiv:1811.00434]

Narjess Afzaly, Scott Morrison, and David Penneys.
The classification of subfactors with index at most 5+1/4.
To appear in Mem. Amer. Math. Soc.
[arXiv:1509.00038]

Scott Morrison and David Penneys.
Monoidal categories enriched in braided monoidal categories.
To appear in Int. Math. Res. Not.
[DOI:10.1093/imrn/rnx217,
arXiv:1701.00567]

Corey Jones and David Penneys.
Operator algebras in rigid C*tensor categories.
Comm. Math. Phys.
355 (2017), no. 3, 11211188.
[arXiv:1611.04620,
DOI:10.1007/s0022001729640]

André Henriques and David Penneys.
Bicommutant categories from fusion categories.
Selecta Math. (NS)
23 (2017), no. 3, 16691708.
[arXiv:1511.05226,
DOI:10.1007/s0002901602510]

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, 39774019.
[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) 10891149
[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, 9991022.
[DOI:10.4153/CJM20150174]
(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 twostrand jellyfish relations.
Pacific J. Math.
277 (2015), no. 2, 463510.
[arXiv:1308.5197,
DOI:10.2140/pjm.2015.2772]

Scott Morrison and David Penneys.
2supertransitive subfactors at index 3+\sqrt{5}
J. Funct. Anal.
269 (2015), no. 9, 28452870.
[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, 729768.
[arXiv:1410.0856,
DOI:10.1007/s0022001524078]

Masaki Izumi, Scott Morrison, David Penneys, Emily Peters, and Noah Snyder.
Subfactors of index exactly 5.
B. Lond. Math. Soc.
(2015) 47 (2): 257269.
[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, 32573298.
[arXiv:1208.3637,
DOI:10.1090/S000299472014061096]

David Penneys.
Chirality and principal graph obstructions.
Adv. Math.
273(19):3255, 2015.
[arXiv:1307.5890,
DOI:10.1016/j.aim.2014.11.021]

Zhengwei Liu, Scott Morrison, and David Penneys.
1supertransitive subfactors with index at most 6+1/5.
Comm. Math. Phys.
334 (2015), no. 2, 889922.
[arXiv:1310.8566,
DOI:10.1007/s0022001421604]

Michael Hartglass and David Penneys.
C*algebras from planar algebras II: the GuionnetJonesShlyakhtenko C*algebras.
J. Funct. Anal. 267 (2014), no. 10, 38593893.
[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. 12, 124.
[arXiv:1208.1564,
DOI:10.1007/s0020801309412]

David Penneys.
A planar calculus for infinite index subfactors.
Comm. Math. Phys.
319 (2013), no. 3, 595648.
[arXiv:1110.3504,
DOI:10.1007/s0022001216274]

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 TemperleyLieb 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), 301337
[arXiv:1007.3173,
DOI:10.4171/QT/23]
Peer reviewed conference proceedings

Corey Jones and David Penneys.
Qsystems and compact W*algebra objects.
2017.
To appear in Contemporary Mathematics.
[arXiv:1707.02155]

Zhengwei Liu, Scott Morrison, and David Penneys.
Lifting shadings on symmetrically selfdual subfactor planar algebras.
2017.
To appear in Contemporary Mathematics.
[arXiv:1709.05023]

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,
344366,
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 André Henriques and James Tener).
Planar algebras in modular tensor categories.
2015.
Oberwolfach Reports.
[DOI:10.4171/OWR/2015/16]
arXiv preprints

André Henriques, David Penneys, and James Tener.
Planar algebras in braided tensor categories.
2016.
[arXiv:1607.06041]

Corey Jones and David Penneys.
Realizations of algebra objects and discrete subfactors.
2017.
[arXiv:1704.02035]

David Penneys.
Unitary dual functors for unitary multitensor categories.
2018.
[arXiv:1808.00323]

Scott Morrison, David Penneys, and Julia Plavnik.
Completion for braided enriched monoidal categories.
2018.
[arXiv:1809.09782]

Pinhas Grossman, Scott Morrison, David Penneys, Emily Peters, and Noah Snyder.
The Extended Haagerup fusion categories.
2018.
[arXiv:1810.06076]

Desmond Coles, Peter Huston, David Penneys, and Srivatsa Srinivas.
The module embedding theorem via towers of algebras.
2018.
[arXiv:1810.07049]
Dissertation
 David Penneys. Planar structure for inclusions of finite von Neumann algebras. 2012. [pdf]
Conference and seminar talks
2019
2018

UCLA 11/15. Functional analysis seminar. The maximal atlas of the Extended Haagerup subfactor

GPOTS,
Miami University (Ohio) 5/296/2.
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

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 4/12.
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 1/2327.
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.
Minicourse on Introduction to subfactor theory.
[course notes (incomplete first draft, posted 2017/2/17)]

AMS Joint Meetings 1/69.
Special Session on Fusion Categories and Quantum Symmetries.
Tensor categories enriched in braided tensor categories
[Beamer slides]
2016
2015

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, 6/297/3.
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, 6/297/3.
C*algebras from planar algebras
[Beamer slides]

GPOTS, Purdue University 5/2630.
Half hour plenary speaker.
The 2D2 subfactor.
[Beamer slides]

USC
Hopf algebras and tensor categories minimeeting 5/2122.
Planar algebras in modular tensor categories

Bodega Bay Subfactor Microconference 5/1617.
Self duality.

UC Berkeley 5/811.
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]
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 9/2226. 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 6/2430. Ostrik's classification of rank 3 pivotal fusion categories
 GPOTS, Kansas State University 5/2731. Half hour plenary speaker. Classifying small index subfactors [Beamer slides]
 Vanderbilt NCGOA 5/28. 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. 1supertransitive subfactors with index at most 6.2
 The Australian National University 3/11. 1supertransitive 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. 1supertransitive 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 5/213. 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 2007present.
Conferences and seminars organized
International and national conferences
 Corey Jones, Henri Moscovici, and I will host the Seventeenth East Coast Operator Algebra Symposium October 1213, 2019 at The Ohio State University.
 Corey Jones and I are organizing the Summer Research Program on Quantum Symmetries June 314, 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 12, 2019.
 Contact organizer for a workshop on Subfactors and fusion categories at BIRS 2018/10/1419 (organized with Gannon, Morrison, and Plavnik)
 Lead for an
American Mathematical Society Mathematics Research Communities
workshop on Quantum symmetries: subfactors and fusion categories, June 1016, 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 1718, 2018
(organized with Julia Plavnik)
 Contact organizer for
Quantum Symmetries: Subfactors and Planar Algebras
July 1721, 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 2017/1/47 (organized with Michael Hartglass and Elizabeth Gillaspy)
 Contact organizer for an AIM SQuaREs workshop 2016/9/1216 (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 2015/10/178 (organized with Vaughan F. R. Jones)
 Wrote a proposal for the workshop Subfactors and Conformal Field Theory at Oberwolfach 2015/03/228 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 2015/1/1112 (organized with Arnaud Brothier, Ionut Chifan, Darren Creutz, and Remus Nicoara)
 Coorganizer for Subfactor Theory in Mathematics and Physics, in honor of the 60th birthday of Vaughan Jones 2014/7/1418 (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 2014/4/138 (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 2014/1/156 (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
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

