Jackson Van Dyke
Office:
02.12.040, TUM Mathematics
Email:
jackson (dot) van-dyke (at) tum.de
I am on the job market for positions starting in Fall 2027!
I did my Ph.D. with
David Ben-Zvi
at UT Austin (May 2024), where my thesis received the Frank Gerth III Dissertation Award,
and am now a postdoc with
Claudia Scheimbauer
at the Technical University of Munich.
Symmetries of quantum field theories are often only projective. This is an instance of a phenomenon physicists call an anomaly.
A basic example is the metaplectic group acting on the quantum harmonic oscillator.
My research studies categorified analogues of this for three- and four-dimensional topological field theories,
where the anomaly is itself an invertible field theory one dimension higher.
Applications include manifold invariants, gapped phases of matter, and the relative Langlands program.
Please don't hesitate to email me
with any corrections, comments, questions, etc.
Papers and preprints
-
Crane-Yetter with background fields: cocycles and skein theory
(joint with Benjamin Haïoun, David Jordan, and Patrick Kinnear) [in progress]
-
Fully extended BF-theory for a continuous group
(joint with Claudia Scheimbauer and Pelle Steffens) [in progress]
-
Invertibility and anomalies of categories of line operators
(joint with Claudia Scheimbauer) [draft available upon request]
-
Fully extended B-models and framing anomalies
(joint with Jurek Bleischwitz) [draft available upon request]
-
Projective symmetries of three-dimensional TQFTs, 2023
[arXiv] [pdf] (Submitted to CMP)
-
Integral transforms for finite gauge theories, 2023
[arXiv] [pdf] (Submitted)
-
Between electric-magnetic duality and the Langlands program
(book with David Ben-Zvi) [pdf] (In preparation)
-
An introduction to knot Floer homology and curved bordered algebras, 2020
(joint with Antonio Alfieri) [arXiv] [journal] (Periodica Mathematica Hungarica)
-
arXiv
Google Scholar
Talks and notes
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TQFTs and representation theory
Mini-Workshop: Higher category theory in geometry and representation theory (Gestalten), Oberwolfach, August 17, 2026
[extended abstract]
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Manifold invariants from higher representation theory
XIV. Bavarian Geometry & Topology Meeting, Universität Regensburg, July 20, 2026
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Equivariant AKSZ theory
Mathematical QFT seminar (joint seminar between TUM and LMU), July 17, 2026
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Equivariant Projective TQFTs
Geometric Representation Theory Seminar, UC Berkeley, November 5, 2025
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Moduli spaces of projective 3d TQFTs
Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras", Max Planck Institute, Bonn, July 7, 2025
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The moduli space of projective 3D TQFTs
Journées de topologie quantique, Paris/Dijon, May 26, 2025
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Extension theory of fusion categories
Scottish Talbot On Algebra and Topology, September 23, 2024
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Anomalies, gauging, and moduli spaces of TQFTs
University of Hamburg, Research seminar - algebra and mathematical physics, September 17, 2024
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Geometric quantization, fusion categories, and Rozansky-Witten theory
University of Lisbon TQFT club, July 31, 2024
[slides]
[video]
-
Projective TQFTs
Technical University of Munich, July 8, 2024
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Projective (symmetries of) TQFTs
University of Hamburg and TU Munich, December 2023
[slides]
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An analogue of the spin extension for fusion categories
Perimeter Institute, July 6, 2023
-
The Drinfeld center and topological symmetries
Simons Collaboration on Global Categorical Symmetries, April 24, 2023
[slides]
-
Spin/Metaplectic extensions for finite 3-dimensional TFTs
UC Davis Geometry/Topology Seminar, April 2022
-
Projectivity, polarization, and a higher Weil representation
Academia Sinica (Taipei, Taiwan) Representation Theory Seminar, March 24, 2022
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Earlier seminar talks
Course notes
Seminar notes
Seminars and conferences
Mentoring
-
Jurek Bleischwitz, Master's thesis, TUM, 2025
Co-supervised with Claudia Scheimbauer. Thesis: A survey of fully extended B-models.
Led to the joint paper Fully extended B-models and framing anomalies.
Miscellaneous (click to expand)
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