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.
2019 OSU Quantum Symmetries summer Research Program June 3-14, 2019
Seventeenth East Coast Operator Algebra Symposium October 12-13, 2019
Mathematics Teaching
- MATH 6211 Real Analysis: Autumn 2019
- MATH 2568 Linear Algebra: Spring 2019, Autumn 2019
- MATH 8160 Quantum Algebra: Autumn 2018 course notes
- MATH 7211 and 7212 Functional Analysis: Autumn 2017 and Spring 2018
- MATH 3345 Foundations of Higher Mathematics: Autumn 2016
Mathematics Research
Peer reviewed journal articles -
André Henriques, David Penneys, and James Tener.
Planar algebras in braided tensor categories.
To appear
*Mem. Amer. Math. Soc.*[arXiv:1607.06041] -
Narjess Afzaly, Scott Morrison, and David Penneys.
The classification of subfactors with index at most 5+1/4.
To appear
*Mem. Amer. Math. Soc.*[arXiv:1509.00038] -
Scott Morrison and David Penneys.
Monoidal categories enriched in braided monoidal categories.
*Int. Math. Res. Not.*2019, no. 11, 3527--3579 [DOI:10.1093/imrn/rnx217, arXiv:1701.00567] -
Corey Jones and David Penneys.
Realizations of algebra objects and discrete subfactors.
*Adv. Math.*350 (2019), p 588-661 [DOI:10.1016/j.aim.2019.04.039, arXiv:1704.02035] -
Marcel Bischoff, Corey Jones, Yuan-Ming Lu, and David Penneys.
Spontaneous symmetry breaking from anyon condensation.
*J. High Energ. Phys.*(2019) 2019: 62. [DOI:10.1007/JHEP02(2019)062, arXiv:1811.00434] -
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] -
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. 2017. To appear in Contemporary Mathematics. [arXiv:1707.02155]
- Zhengwei Liu, Scott Morrison, and David Penneys. Lifting shadings on symmetrically self-dual 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, 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 André Henriques and James Tener). Planar algebras in modular tensor categories. 2015. Oberwolfach Reports. [DOI:10.4171/OWR/2015/16]
- 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]
- Corey Jones, Scott Morrison, David Penneys, and Julia Plavnik. Extension theory for braided-enriched fusion categories 2019. [arXiv:1910.03178]
- David Penneys. Planar structure for inclusions of finite von Neumann algebras. 2012. [pdf]
Conference and seminar talks
2020 - Concentration Week on Quantum Groups, Tensor Categories, and Subfactors, July 27-31, 2020. Introduction to the classification program for subfactors
- MSRI Connections for Women: Quantum Symmetries 1/23-24. TBD
- 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 - 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.
- 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 - 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: 2019/10/9 |