Articles
Articles
"We prove a conjecture of Lurie characterizing (n+1)-dualizability in higher Morita categories of En-algebras in terms of dualizability over certain factorization homologies. A key ingredient is a higher Morita category based on the recently developed framework of pointless factorization algebras of Karlsson and the first author. We also verify an invertibility conjecture of Brochier--Jordan--Safranov--Snyder as an immediate corollary of our main result.
Moreover, we prove a relative version of the dualizability conjecture, yielding a new criterion for relative/twisted field theories. We give some examples, including Dirichlet and Neumann relative theories."
String nets for twisted pivotal categories, arXiv:2605.28650, with Benjamin Haïoun and Filippos Sytilidis
"We develop a graphical calculus for monoidal categories equipped with twisted pivotal structures, which are a generalization of pivotal structures originating from the study of orientation structures in the context of the Cobordism Hypothesis.
This graphical calculus depends on a possibly singular foliation, and we use it to construct twisted string net modules for surfaces equipped with a Morse function or a Morse foliation. We prove that, despite the apparent dependence on this Morse function, the twisted string net modules assemble in an oriented categorified 2-TQFT.
We study when the twisted string net module of the 2-sphere vanishes, relate it to the distinguished invertible object for finite tensor categories and exhibit examples of non-unimodular finite tensor categories with non-vanishing twisted string net module on the 2-sphere. This vanishing is expected to be the main obstruction for extending our categorified 2-TQFT to a non-compact 3-TQFT."
"The Nappi–Witten model is a Wess–Zumino–Witten model in which the target space is the nonreductive Heisenberg group H4. We consider the representation theory underlying this conformal field theory. Specifically, we study the category of weight modules, with finite-dimensional weight spaces, over the associated affine vertex operator algebra H4. In particular, we classify the irreducible H4-modules in this category and compute their characters. We moreover observe that this category is nonsemisimple, suggesting that the Nappi–Witten model is a logarithmic conformal field theory."
In preparation
I have the following papers currently in preparation, a large portion of which is contained in my PhD thesis.
A topological approach to relative field theories (incl. material from Chapters 9 and 10 of my PhD thesis)
On the defect cobordism hypothesis (incl. material from Chapters 5 and 8 of my PhD thesis)
Domain walls and oplax natural transformations (incl. material from Chapters 3, 6, and 7 of my PhD thesis)
Theses
I completed my PhD thesis at UT Austin in August 2024 under the supervision of Dan Freed. My thesis was titled "Topological domain walls and relative field theories". You can find a copy here.
I completed my Master's thesis titled "On the twisted sector of Wess-Zumino-Witten models" at the University of Melbourne in October 2017 under the supervision of David Ridout. You can find a copy of my Master's thesis here.
Talks and presentations
Constructing oriented TQFTs from twisted pivotal tensor categories, April 2026, Purdue Topology Seminar (online)
Constructing oriented TQFTs from twisted pivotal tensor categories, February 2026, Harvard CMSA Geometry and Quantum Field Theory Seminar
Constructing oriented TQFTs from twisted pivotal tensor categories, February 2026, Generalized Symmetries and Defects in QFT and Gravity, Aspen Center for Physics
Categorical Approaches to Defects, December 2025, University of Vienna
Relative homotopy field theories, November 2025, Simons Foundation on Global Categorical Symmetries Annual Pre-Meeting, NYU
Relative dualizability in higher Morita categories (poster presentation), July 2025, Spaces of tensor categories, ICMS
Relative dualizability of factorization algebras, July 2025, Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras, MPIM Bonn
Boundaries of non-semisimple TQFTs, December 2024, Tensor Categories, Quantum Symmetries and Mathematical Physics, MATRIX
Domain walls and oplax natural transformations, October 2024, RHIND Seminar, LMU Munich
A geometric construction of relative field theory, August 2023, Higher structures on functorial field theory, University of Regensburg
Topological symmetries and boundary theories, April 2023, Global Categorical Symmetries Postdoc and PhD Colloquim (online)
Boundary data for topological field theories, December 2022, Mathematical Physics Seminar, University of Melbourne
Relative field theories (poster presentation), June 2022, Global Categorical Symmetries Conference and Summer School, Perimeter Institute
On the twisted sector of Wess-Zumino-Witten models, February 2018, ANZAMP Annual Meeting, Auckland