# Marcel Bischoff

This webpage is now hosted at localconformal.net.

I am Assistant Professor in Mathematics at Ohio University, Athens, OH.
Before that, I was PostDoc (non-tenure track Assistant Professor) in Mathematics at Vanderbilt University, Nashville, TN, where my supervisor is Vaughan Jones.
My research interests are Operator Algebras, in particular Subfactors, Algebraic Quantum Field Theory, in particular Conformal Field Theory and Tensor Categories.
I am principal investigator of
NSF Grant DMS-1821162 *Quantum Symmetries and Conformal Nets* (former
NSF Grant DMS-1700192).

## Contact

Office: Morton Hall 521

Office hours: TBD

Tel: 740-593-1261

eMail:

Department of Mathematics

Morton Hall 321

1 Ohio University

Athens, OH 45701

## Teaching

2019- Fall 2019-2020: Math 6301: Analysis I (MWF 9:40-10:35)
- Spring 2018-2019: Math 6302: Analysis II (MWF 9:40-10:35)

- Fall 2018-2019: Math 6301: Analysis I (MWF 9:40-10:35)
- Spring 2017-2018 (Ohio University): Math 3200/5200: Applied Linear Algebra (MWF 12:55-1:50)
- Spring 2017-2018 (Ohio University): Math 6710: Algebraic Topology (MWF 3:05-4:00)

- Fall 2017 (Ohio University): Math 3210/5210: Linear Algebra (MWF 11:15-12:55)
- Spring 2017 (Vanderbilt): Math 3110: Complex Variables (TR 11-12:15)

- Fall 2016 (Vanderbilt): Math 2600-02: Linear Algebra (MWF 2:10-3p)
- Spring 2016 (Vanderbilt): Math 3110: Complex Variables

- Fall 2015 (Vanderbilt): Graduate Course: Algebraic and Topological Quantum Field Theory
- Spring 2015: Math 196: Differential Equations with Linear Algebra

- Fall 2014 (Vanderbilt): Math 155A-23/24 (Recitations)

## Seminars

Ohio University Analysis Seminar (I am a co-organizer).

Quantum Algebra and Quantum Topology Seminar (OSU)

Subfactor Seminar Spring 2018 (at Vanderbilt University)

Semester schedule (TODO)

## Events and Upcoming Talks

2020- 01/16/2019 - 01/19/2019: Joint Mathematics Meetings 2020, Denver, CO.
- Invited talk:
*Conformal subnets and compact hypergroups*at AMS Special Session on Mathematical Aspects of Conformal Field Theory (01/18/2019)

- Invited talk:

## Past Events and Given Talks

2019- 11/09/2019 - 11/10/2019 AMS Fall Western Sectional Meeting, University of California, Riverside, Riverside, CA.
- Invited talk:
*Local discrete subfactors and hypergroup actions*(11/09/2019) in a Special Session on "Advances in Operator Algebras".

- Invited talk:
- 10/27/2019 - 11/02/2019: Oberwolfach Workshop 1944 "Subfactors and Applications",
Mathematisches Forschungsinstitut Oberwolfach, Germany.
- Talk:
*Quantum Operations on Conformal Nets**(10/29/2019)*

- Talk:
- 08/22/2019: Quantum Topology and Quantum Algebra Seminar, The Ohio State University, Columbus, OH.
- 06/24/2019 - 06/30/2019: Operator Algebras and Quantum Physics, Simons Center For Geometry and Physics, Stony Brook, NY.
- Invited talk:
*Quantum Operations on Conformal Nets and Twisted Representations*(06/25/2019) [Video]

- Invited talk:
- 01/16/2019 - 01/19/2019: Joint Mathematics Meetings 2019, Baltimore, MD.
- Invited talk:
*Symmetry breaking from anyon condensation*at AMS Special Session on Quantum Symmetries: Subfactors and Fusion Categories (a Mathematics Research Communities Session) (01/17/2019)

- Invited talk:
- 01/08/2019: Quantum Topology and Quantum Algebra Seminar, The Ohio State University, Columbus, OH.

*2018*- 08/28/2018: Quantum Topology and Quantum Algebra Seminar, The Ohio State University, Columbus, OH.
- 10/14/2018 - 10/19/2019: BIRS Workshop 18w5195, Fusion Categories and Subfactors, Banff, Canada.
- 07/29/2018 - 08/03/2018: BIRS Workshop 18w5015, Physics and Mathematics of Quantum Field Theory, Banff, Canada.
- 06/10/2018 - 06/16/2018: MRC Quantum Symmetries: Subfactors and Fusion Categories, West Greenwich, RI.
- 04/28/2018: OHIO Conference, Columbus, OH
- Co-Organizer
- Talk:
*Completely Positive Actions on Local Nets of Observables*

- 04/13/2018-04/15/2018: Vanderbilt University, Nashville, TN.
- Seminar Talk:
*Infinite Index Subfactors from Conformal Inclusions*, Subactor Seminar

- Seminar Talk:
- 04/14/2018 - 04/15/2018: AMS Sectional Meeting at Vanderbilt University, Nashville, TN.
- Invited Talk:
*Generalized Twisted Orbifold Construction)*(04/15/2018) at Special Session on Advances in Operator Algebras - Co-Organizer: Special Session on Tensor Categories and Diagrammatic Methods

- Invited Talk:
- 04/01/2018 - 04/05/2018: Visiting Harvard University, Camebridge, MA.
- Seminar Talk: Quantum Symmetries and Conformal Nets (04/03/2018)

- 03/17/2018 - 03/18/2018: AMS Sectional Meeting at The Ohio State University, Columbus, OH.
- Invited Talk:
*A Notion of Quantum Symmetry.*(03/17/2018) at Special Session on "Quantum Symmetries" `

- Invited Talk:
- 01/10/2018 - 01/13/2018: Joint Mathematics Meetings 2018, San Diego, CA.
- Co-organizer: AMS Special Session on Advances in Operator Algebras (01/12-01/13/2018).

- 11/26/2017 - 12/02/2017: Oberwolfach Workshop 1748 "Reflection Positivity", Mathematisches Forschungsinstitut Oberwolfach, Germany.
- 11/16/2017: Going to: Noncommutative Geometry and Operator Algebra seminar, The Ohio State University, Columbus, OH.
- 11/04/2017 - 11/05/2017: AMS Fall Western Sectional Meeting
University of California, Riverside, Riverside, CA.
- Invited Talk:
*On Generalized Metaplectic Modular Categories (11/04/2017 9:30am)*at Special Session on Tensor Categories: Bridging Algebra, Topology, and Physics - Invited Talk:
*Quantum Operations on Conformal Nets*(11/04/2017 4:30pm) at Special Session on Advances in Operator Algebras

- Invited Talk:
- 10/29/2017 - 10/31/2017: Visiting Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada.
- Invited Talk: On Generalized Orbifolds in Conformal Quantum Field Theory (10/30/2017)

- 10/24/2017: Seminar Talk:
*On Generalized Metaplectic Modular Categories*, Quantum Algebra & Quantum Topology Seminar, The Ohio State University, Columbus, OH. - 09/30/2017 - 10/01/2017: Workshop "Subfactors and Applications", Vanderbilt University, Nashville, TN.
- 09/19/2017 - 09/22/2017:
Advances in Mathematics and Theoretical Physics, Palazzo Corsini, "Accademia dei Lincei", Rome, Italy.
- Invited Plenary Talk:
*Symmetries in Quantum Field Theories Beyond Groups*

- Invited Plenary Talk:
- 07/17/17 - 07/24/17: Quantum Symmetries: Subfactors and Planar Algebras, Maui, HI.
- Invited Talk:
*Quantum Symmetries of Conformal Nets*(07/21/2017)

- Invited Talk:
~~01/09/2017 - 06/23/2017 (TBD): Operator Algebras: Subfactors and their Applications, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.~~~~06/12/2017 - 06/16/2017: Workshop: Subfactors, K-theory and Conformal Field Theory, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.~~~~Invited Talk:~~*TBA*

- 06/03/17 - 06/04/17: Hopf Algebras and Tensor Categories in San Diego - Summer 2017 West Coast Lie Theory Workshop, San Diego, CA.
- Invited Talk:
*Symmetries of conformal nets beyond groups*

- Invited Talk:
~~04/28/2017: (TBC) Seminar Talk at Perimeter Institute~~(postponed)~~04/04/2017 - 04/07/2017: Quantum Field Theory: Concepts, Constructions & Curved Spacetimes, York, UK.~~~~Invited Talk:~~*Symmetries in QFT beyond groups*

- 04/01/2017 - 04/02/2017: AMS Sectional Meeting at Indiana University, Bloomington, IN.
- Invited Talk:
*Realizability of Tambara-Yamagami Categories by Conformal Nets*at AMS Special Session on "Fusion categories and applications" (Special Session #26A)

- Invited Talk:
- 03/03/2017: Colloquim Talk:
*Subfactors and Conformal Nets*at Ohio University, Athens, OH. - 02/23/2017: Seminar Talk:
*Defects in Algebraic Quantum Field Theory*at UC Davis. - 02/22/2017: Seminar Talk:
*Fusion Categories from Subfactors and Conformal Nets*at UCSD. - 01/27/2017: Colloquium Talk
*Subfactors, Fusion Categories and Conformal Nets*at LSU, Baton Rouge, LA. - 01/04/2017 - 01/07/2017: Joint Mathematics Meetings 2017, Atlanta, GA.
- Invited Talk:
*Generalized fixed points of conformal nets*at AMS Special Session on Advances in Operator Algebras, I [slides]

- Invited Talk:

- 11/14/2016 - 11/23/2016:
Berkeley-Tokyo Autumn School - Quantum Field Theory and Subfactors.
UC Berkeley, CA.
- Invited Lectures:
*Conformal Nets and Tensor Categories I-III* - Notes: Lecture I

- Invited Lectures:
- 11/01/2016 - 11/03/2016: Visting: The Ohio State University, Columbus, OH.
Columbus, OH.
- Invited talk:
*Generalized orbifold construction for conformal nets*, Noncommutative Geometry Seminar. - Invited talk:
*Extensions of modular tensor categories and subtheories in conformal field theory*, Quantum Algebra & Quantum Topology Seminar

- Invited talk:
- 10/08/2016 - 10/10/2016: Workshop on Subfactors, Quantum Field Theory and Quantum Information, Harvard University, Cambridge, MA.
- 10/01/2016 - 10/02/2016: East Coast Operator Algebras Symposium 2016, Loyola University, Chicago, IL.
- 09/20/2016: Invited Talk at Algebra seminar:
*Generalized Orbifolds in Conformal Field Theory*, Emory University, Atlanta, GA. - 07/24/2016 - 07/30/2016: Oberwolfach Workshop 1630 "Recent Mathematical Developments in Quantum Field Theory", Mathematisches Forschungsinstitut Oberwolfach, Germany.
- 07/04/2016 - 07/08/2016:
Workshop "Von Neumann Algebras",
HIM, Bonn, Germany.
- Invited Talk:
*Generalized fixed points of conformal nets and quantum double subfactors*

- Invited Talk:
- 07/01/2016 - 07/24/2016:
Hausdorff Trimester Program: Von Neumann Algebras (Trimester: 05/02/2016 - 08/26/2016),
HIM, Bonn, Germany.
- Invited Talk:
*Defects and Phase boundaries in Algebraic Conformal Quantum Field Theory*- Trimester Semimar (07/20/2016)

- Invited Talk:
- 06/27/2016 - 07/01/2016: Mathematics and Physics at the Crossroad, INFN, Frascati, Italy.
- 06/27/2016 - 06/29/2016:
Operator Algebras and Quantum Field Theory - Dedicated to the memory of John E. Roberts,
INFN - Laboratori Nazionali di Frascati, Italy.
- Invited Talk:
*Conformal nets, alpha-induction and defects*

- Invited Talk:
- 05/27/2016 - 05/28/2016:
38th LQP Workshop "Foundations and Constructive Aspects of QFT", TU München, Munich, Germany.
- Talk:
*Generalized Orbifolds in Algebraic Conformal QFT*(05/27/2016) [slides]

- Talk:
- 05/17/2016 - 05/25/2016: NCGOA Spring Institute 2016, HIM, Bonn, Germany.
- 05/08/2016 - 05/26/2016 Hausdorff Trimester Program: Von Neumann Algebras (Trimester: 05/02/2016 - 08/26/2016), HIM, Bonn, Germany. [Video]
- 04/09/2016 - 04/10/2016: AMS
Spring Western Sectional Meeting University of Utah, Salt Lake City, UT.
- Invited Talk:
*Conformal nets and unitary fusion categories*at Special Session on Fusion Categories and Topological Phases of Matter.

- Invited Talk:
- 04/01/2016 Talk in Subfactor Seminar:
*Commutative Algebras in Braided Tensor Categories and Quantum Symmetries*, Vanderbilt University, Nashville, TN. - 03/07/2016 - 03/11/2015: Visiting: University of California Los Angeles.
- Talk:
*Subfactors and Defects in Conformal Field Theory*

- Talk:
- 01/06/2016 - 01/09/2016: Joint Mathematics Meeting 2016, Seattle, WA.
- Co-organizer: AMS Special Session on Classification Problems in Operator Algebras (01/08/2016).

- 12/07/2015 - 12/10/2015: First joint meeting SBM - SBMAC - RSME, Universidade Federal do Ceará, Fortaleza, Brazil.
- Invited Talk:
*Conformal Nets, Defects and Realization of Quantum Doubles*in Special Session:*Operator Algebras*

- Invited Talk:
- 11/06/2015 Talk in Subfactor Seminar:
*Generalized Orbifold Construction for Conformal Nets*, Vanderbilt University, Nashville, TN. - 10/17/2015 - 10/18/2015: AMS Sectional Meeting at the University of Memphis in Memphis, TN.
- Invited Talk:
*Quantum Doubles and Conformal Field Theory*(10/17/2015)

- Invited Talk:
- 10/10/2015 - 10/11/2015: West Coast Operator Algebra Seminar, University of California, San Diego, CA.
- 07/13/2015 - 07/17/2015: International Conference On Subfactor Theory in Mathemhematics and Physics, Quinhuangdao, China.
- 07/06/2015 - 07/12/2015: Visiting University of Tokyo, Japan.
- Invited talk (FMPS Lecture):
*Conformal Field Theory, Subfactors and Planar Algebras*(07/08/2015)

- Invited talk (FMPS Lecture):
- 05/26/2015 - 05/30/2015: GPOTS 2015,
Purdue University, West Lafayette, IN.
- Contributed talk:
*A planar algebraic description of defect lines in conformal field theory*(05/26/2015) [slides]

- Contributed talk:
- 05/01/2015 - 05/07/2015: NCGOA Spring Institute 2015 - Operator Algebras and Approximation Properties of Groups, Department of Mathematics - Vanderbilt University, Nashville TN.
- 03/22/2015 - 03/28/2015: Oberwolfach Workshop 1513 "Subfactors and Conformal Field Theory",
Mathematisches Forschungsinstitut Oberwolfach, Germany.
- Invited talk:
*An Algebraic Conformal Quantum Field Theory Approach to Defects*(03/28/2015)

- Invited talk:
- 01/10/2015 - 01/13/2015: Joint Mathematics Meeting, San Antonio, TX.

- 10/31/2014: Explanatory Talk in Subfactor seminar "Realizing representation categories of compact groups in higher dimensional quantum field theories" (after Doplicher, Piacitelli), Vanderbilt University.
- 09/05/2014: Talk in Subfactor seminar "A center construction for braided subfactors and defects of conformal nets", Vanderbilt University.
- 07/21/2014: Talk in QFT seminar "VOA approach to CQFT", University of Göttingen.
- 05/19/2014 - 05/23/2014: Algebraic Quantum Field Theory - Its status and its future, ESI - Vienna.
- 05/11/2014 - 05/16/2014: University of California Berkeley, Department of Mathematics, Berkeley, CA.
- 05/14/2014: Seminar Talk: "(Re-)constructing VOAs from Conformal Nets" [Notes]

- 05/02/2014 - 05/08/2014: NCGOA Spring Institute 2014 - Subfactors, CFT, and VOA, Department of Mathematics - Vanderbilt University, Nashville TN.
- 05/08/2014: Invited talk: "Topological Defects and Phase Boundaries in Algebraic Conformal Quantum Field Theory" [slides]

- 03/18/2014 - 03/20/2014: DPG Spring Meeting, Berlin.
- 03/20/2014 Talk: "Phase Boundaries in Algebraic Conformal QFT"

- 12/01/2013 - 12/04/2013: Visiting: Fachbereich Mathematik - Universtität Hamburg.
- 11/27/2013 - 11/29/2013: Lecture Series: A solvable (noncommutative) QFT in 4 dimensions, Universität Göttingen.
- 11/14/2013 - 11/16/2013: 33rd Workshop
"Foundations and Constructive Aspects of QFT", Göttingen, Germany,
- Co-organization

- 10/07/2013 - 10/10/2013: Second Erlangen Fall School on Quantum Geometry, Erlangen, Germany.
- 07/08/2013 - 07/12/2013: Mathematics and Quantum Physics, Roma, Accademia dei Lincei.
- 05/31/2013 - 06/01/2013: 32nd Workshop
"Foundations and Constructive Aspects of QFT", Bergische Universität Wuppertal.
- Talk: "Characterization of rational conformal QFTs and their boundary conditions" [slides]

- 04/26/2013: Seminar Talk about Braided Subfactors and CFT in the Higher Structures seminar, Universität Göttingen.
- 03/14/2013: Meeting of Research Training Groups 1463 (Hannover), 1493 (Göttingen), 1670 (Hamburg) in Hannover.
- 02/26/2013 - 02/28/2013: DPG Frühjahrstagung in Jena, Germany.
- 01/18/2013 - 02/01/2013: Visiting Graduate School of Mathematical
Sciences, University of Tokyo.
- 01/30/2013: Miniworkshop on Operator Algebras III, Graduate School of Mathematical Sciences, University of Tokyo.
- Invited talk: "Construction of models in low dimensional QFT using operator algebraic methods"

- 12/11/2012 - 12/13/2012: Mathematical
Physics Trimester at
Hausdorff Research Institute for Mathematics, Bonn.
- 12/12/2012: Invited talk: "Characterization of 2D conformal quantum field theories and their boundary conditions"

- 11/23/2012 - 11/24/2012: 31st Workshop "Foundations and Constructive Aspects of QFT", Universität Leipzig.
- 07/30/2012 - 08/01/2012: Mathematical Aspects of Quantum Field Theory and Quantum Statistical Mechanics, Hamburg, Germany.
- 05/04/2012 - 05/10/2012: Conformal Field Theory and von Neumann Algebras, Vanderbilt University.
- 02/27/2012 - 03/02/2012: DPG Frühjahrstagung in Göttingen, Germany.
- 02/06/2012: Quantum Field Theory seminar of the Institute of Theoretical Physics, University of Göttingen.
- Seminar talk: "Construction of two-dimensional QFTs by Longo-Witten endomorphisms of chiral QFTs"

- 11/18/2011 - 11/19/2011: 29th Workshop "Foundations and Constructive Aspects of QFT",
Universität Leipzig.
- Talk: "Longo-Witten Endomorphisms and Construction of Wedge-Local Nets" (11/18/2011)

- 07/01/2011 - 07/02/2011: 28th Workshop "Foundations and Constructive Aspects of QFT", Universität Göttingen.
- 05/30/2011 - 06/01/2011: Meeting of GDRE GREFI-GENCO
Paris
Institut Henri Poincaré
- Talk: "Semigroup elements associated to conformal nets and boundary quantum field theory" (06/01/2011) [slides]

- 04/25/2011 - 04/30/2011: EU - NCG 4th Annual Meeting in Bucharest, Romania.
- Talk: "Local nets on Minkowski half-plane associated to lattices" (04/29/2011) [slides]

- 03/28/2011 - 04/01/2011: DPG Frühjahrstagung in Karlsruhe Germany.
- Talk: "Construction of Models in Boundary Quantum Field Theory" (03/31/2011)

- 01/10/2010 - 01/11/2010: CMTP Workshop "Two Days in QFT", Rome.
- 09/22/2010 - 09/25/2010: Seminal Interactions Between Mathematics and Physics, Accademia Nazionale dei Lincei, Roma.
- 08/16/2010 - 08/21/2010:
Workshop: Operator Algebras and
Conformal Field Theory, University of Oregon, Eugene OR.
- Explanatory talk: "Modularity of the category of representations of a conformal net (Part 2)" (08/21/2010)
- [notes] taken from the TeXed notes compiled by Emily Peters

- 06/18/2010 - 06/19/2010: 26th Workshop "Foundations and Constructive Aspects of QFT", Mathematisches Institut der Westfälischen Wilhelms-Universität, Münster, Germany.

## Links

### People (collaborators, etc.)

Wojciech Dybalski

Olivier Gabriel

Terry Gannon

André Henriques

Corey Jones

Vaughan F. R. Jones (Vanderbilt) (Berkeley)

Yasuyuki Kawahigashi

Roberto Longo

Pierre Martinetti

Dave Penneys

Karl-Henning Rehren

Yoh Tanimoto

Gennaro Tedesco

James Tener

### Lists of Conferences (mainly operator algebras)

Paul Pinto

Michael Anshelevich

Narutaka Ozawa

### Various

arXiv

MathSciNet (restricted access)

Local Quantum Physics Crossroads

LQP 2 (beta)

mathoverflow

Theoretical Physics Stackexchange

### Online Resources

The online database of Vertex Operator Algebras and Modular Categories (Version 0.5)

AIM Open Problem List: Fusion Categories

Atlas of subfactors

ATLAS of finite group representations

The On-Line Encyclopedia of Integer Sequences™ (OEIS™)

A Catalogue of Lattices

Schelleken's Kac

Wolfram alpha

Online INteGratOr

Resolve a DOI name

Create a PDF calendar online

### Me

Ohio Unviersity Mathematics Department

arXiv.org

ORCID: 0000-0001-5509-5762

Google Scholar

lqp2.org

Research Gate

mathoverflow.net

zbMATH

Mathematics Genealogy Project

### Internal

Last update:
2020-01-08 15:04:51. My Erdős number happens to be ~~5~~ 4.