research interests
My research area is mathematical physics. I work on fully extended topological field theories (in the sense of Lurie) using higher category theory, factorization algebras/homology, and derived symplectic geometry. I am also interested in relative, or twisted, field theories in the sense of FreedTeleman and StolzTeichner, in particular as realizing (possibly noninvertible) symmetries. I have worked on several questions revolving around objects carrying a higher categorical structure called "2Segal object" which was introduced by DyckerhoffKapranov and GàlvezCarrilloKockTonks and generalizes the idea of a categorical structure with a multivalued composition. These questions include applications in topology (Waldhausen construction and Ktheory, configuration spaces) and mathematical physics (modular functors).
articles
Assembly of Constructible Factorization Algebras, arXiv:2403.19472
with Eilind Karlsson and Tashi Walde
We provide a toolbox of extension, gluing, and assembly techniques for factorization algebras. Using these tools, we fill various gaps in the literature on factorization algebras on stratified manifolds, the main one being that constructible factorization algebras form a sheaf of symmetric monoidal ∞categories. Additionally, we explain how to assemble constructible factorization algebras from the data on the individual strata together with module structures associated to the relative links; thus answering a question by Ayala. Along the way, we give detailed proofs of the following facts which are also of independent interest: constructibility is a local condition; the ∞category of disks is a localization of any sufficiently fine poset of disks; constructibility implies the Weiss condition on disks. For each of these, variants or special cases already existed, but they were either incomplete or not general enough.
Dagger ncategories, arXiv:2403.01651
with Giovanni Ferrer, Brett Hungar, Theo JohnsonFreyd, Cameron Krulewski, Lukas Müller, Nivedita, David Penneys, David Reutter, Luuk Stehouwer, Chetan Vuppulury
We present a coherent definition of dagger (∞,n)category in terms of equivariance data trivialized on parts of the category. Our main example is the bordism higher category BordXn. This allows us to define a reflectionpositive topological quantum field theory to be a higher dagger functor from BordXn to some target higher dagger category C. Our definitions have a tunable parameter: a group G acting on the (∞,1)category Cat(∞,n) of (∞,n)categories. Different choices for G accommodate different flavours of higher dagger structure; the universal choice is G=Aut(Cat(∞,n))=(Z/2Z)n, which implements dagger involutions on all levels of morphisms. The Stratified Cobordism Hypothesis suggests that there should be a map PL(n)→Aut(AdjCat(∞,n)), where PL(n) is the group of piecewiselinear automorphisms of Rn and AdjCat(∞,n) the (∞,1)category of (∞,n)categories with all adjoints; we conjecture more strongly that Aut(AdjCat(∞,n))≅PL(n). Based on this conjecture we propose a notion of dagger (∞,n)category with unitary duality or PL(n)dagger category. We outline how to construct a PL(n)dagger structure on the fullyextended bordism (∞,n)category BordXn for any stable tangential structure X; our outline restricts to a rigorous construction of a coherent dagger structure on the unextended bordism (∞,1)category BordXn,n−1. The article is a report on the results of a workshop held in Summer 2023, and is intended as a sketch of the big picture and an invitation for more thorough development.
Relative field theories via relative dualizability, arxiv:2312.0505
with Thomas Stempfhuber
We investigate relative versions of dualizability designed for relative versions of topological field theories (TFTs), also called twisted TFTs, or quiche TFTs in the context of symmetries. In even dimensions we show an equivalence between lax and oplax fully extended framed relative topological field theories valued in an (∞,N)category in terms of adjunctibility. Motivated by this, we systematically investigate higher adjunctibility conditions and their implications for relative TFTs. Summarizing we arrive at the conclusion that oplax relative TFTs is the notion of choice. Finally, for fun we explore a tree version of adjunctibility and compute the number of equivalence classes thereof.
The AKSZ construction in derived algebraic geometry as an extended topological quantum field theory, accepted for publication in Memoirs of the AMS, arxiv:2108.02473
with Damien Calaque and Rune Haugseng
We combine tools from extended topological field theories, derived algebraic geometry and higher categories to prove that the AKSZ construction of shifted symplectic forms on σmodels, i.e.~derived mapping stacks extends to a fully extended semiclassical TFT. This extends work by Pantev—Toën—Vaquié—Vezzosi and Calaque. The construction is two fold: on the one hand, they show full dualizability and use the Cobordism Hypothesis; on the other hand, they exhibit the symmetric monoidal functor in question, thus demonstrating the Cobordism Hypothesis in action. Examples include classical Chern–Simons theory, classical Rozansky–Witten theory, and the Poisson sigma model.
Comparison of Waldhausen constructions, Ann. KTheory 6 (2021), no. 1, 97–136, arxiv:1901.03606
with Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova, and Martina Rovelli
We generalize our previous, discrete, result to the homotopical setting, by showing that there is a Quillen equivalence between a model category for unital 2Segal objects and a model category for augmented stable double Segal objects which is given by an Sconstruction.
2Segal objects and the Waldhausen construction, Algebr. Geom. Topol. 21 (2021), no. 3, 1267–1326, arxiv:1809.10924
with Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova, and Martina Rovelli
We generalize our previous, discrete, result to the homotopical setting, by showing that there is a Quillen equivalence between a model category for unital 2Segal objects and a model category for augmented stable double Segal objects which is given by an Sconstruction.
The edgewise subdivision criterion for 2Segal objects, Proc. Amer. Math. Soc., 148(1):71–82, arxiv:1807.05069
with Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova, and Martina Rovelli
We show that the edgewise subdivision of a 2Segal object is always a Segal object, and furthermore that this property characterizes 2Segal objects.
Duals and adjoints in the factorization higher Morita category arxiv:1804.10924
with Owen Gwilliam
We study dualizability in the factorization (∞,n+N)Morita category Alg_n(S) of E_nalgebras, bimodules in E_{n1}algebras, bimodules of bimodules, etc. in an (∞,N)category S. More precisely, we that the symmetric monoidal (∞,n)category underlying Alg_n(S) is fully ndualizable, i.e. every object has a dual and every kmorphism has a left and a right adjoint for 0 < k < n. The Cobordism Hypothesis gives an immediate application of this result, namely the existence of categorified ndimensional topological field theories (which were constructed explicitly in my PhD thesis using factorization homology, see below), and relative versions thereof. The motivation for this result was to construct lowdimensional examples of relative, "twisted", field theories in a subsequent article.
2Segal sets and the Waldhausen construction, Topology and its Applications 23 (2018) pp. 445484, arxiv:1609.02853
with Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova, and Martina Rovelli
We give a variant of Waldhausen's Sconstruction which allows to take in certain double categories and showed that this is an equivalence of categories to the category of multivalued categories (unital 2Segal sets). An extension of this construction to the homotopical setting should appear soon in a followup project.
(Op)lax natural transformations, twisted quantum field theories, and "even higher" Morita categories, Advances in Mathematics 307 (2017) pp. 147223, arxiv:1502.06526
with Theo JohnsonFreyd
The main motivation for this project was to give a precise definition of twisted field theories in the setting of higher categories. This led to the development of a framework for lax and oplax transformations and their higher analogs between strong (∞,n)functors. Another motivation was to give a construction of the higher Morita category of E_dalgebras in a symmetric monoidal (∞,n)category C as an (∞,n+d)category, thus extending the construction of my thesis below. Examples include the (∞,4)category of braided monoidal (nice, linear) categories, monoidal bimodule categories, bimodule categories, functors, and natural transformations.
A note on the (∞,n)category of cobordisms, Algebr. Geom. Topol., 19(2):533–655, 2019, arxiv:1509.08906
with Damien Calaque
Inspired by Lurie's paper on the cobordism hypothesis we define an nfold Segal space of cobordisms, which is a good model for the (∞,n)category of cobordisms.
Lectures on mathematical aspects of (twisted) supersymmetric gauge theories, Mathematical Aspects of Quantum Field Theories, Damien Calaque and Thomas Strobl, editors, Mathematical Physics Studies. Springer International Publishing, 2015, arxiv:1401.2676
with Kevin Costello
These are lecture notes I wrote for talks by Kevin Costello at the Winter School in Mathematical Physics 2012.
in preparation

A universal property of the higher category of spans and finite homotopy theories and a fully extended TFT (with Tashi Walde)

A recognition principle for chain complexes of E_nalgebras (with Grégory Ginot, Tashi Walde)

States and observables in lowdimensional topological field theory (with Owen Gwilliam)

Factorization homology as a fully extended topological field theory (with Damien Calaque)
thesis
Factorization homology as a fully extended topological field theory
We first give a precise definition of a fully extended ndimensional topological field theory using complete nfold Segal spaces as a model for (∞,n)categories and then, given an E_nalgebra A, we explicitly construct a fully extended TFT given by taking factorization homology with coefficients in A. This is the fully extended nTFT corresponding (via the cobordism hypothesis) to the E_nalgebra A, which is a fully dualizable object in a suitable Morita(∞,n)category Alg_n of E_n algebras.
Some notes from my talk at the Winter School in Mathematical Physics 2014 in Les Diablerets. A video of a talk I gave about my thesis is available here.
Here is the current version of my thesis on "Factorization Homology as a Fully Extended Topological Field Theory".
extended abstracts and slides
 Quantum field theory meets Higher Categories, talk in the "North meets South Colloquium" at the Mathematical Insitute, University of Oxford, May 2018
 Quantum field theory meets Topology, talk at the Oxford Alumni Weekend representing the Mathematical Insitute, September 2017
 A factorization view on states and observables, talk at StringMath 2017 in Hamburg, July 2017
 Derived symplectic geometry and AKSZ topological field theories, talk at Algebra and Geometry meeting in Barcelona, December 2016
 2Segal spaces and the Waldhausen construction, Oberwolfach Report no. 35, 2016, Workshop Topologie
 Factorization algebras and (twisted) functorial field theories  the topological case, Oberwolfach Report no. 25, 2016, Workshop Factorization Algebras and Functorial Field Theories