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 openclosed field theories in the sense of Costello and Lurie and relative, or twisted, field theories in the sense of FreedTeleman and StolzTeichner. Recently, I have become interested in 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
The AKSZ construction in derived algebraic geometry as an extended topological quantum field theory 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 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 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, accepted for publication in Proceedings of the AMS, 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

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