Research

Publications and preprints

1. An equivalence theorem for algebraic and functorial QFT, with J. MacManus and A. Schenkel, 39pp., arXiv:2504.15759.
   Proves that the algebraic and bordism-based approaches to quantum field theory on Lorentzian manifolds are equivalent.

2. The local moduli space of the Einstein-Yang-Mills system, with C. S. Shahbazi and V. Muñoz, Asian J. Math., 29(2):201-252 (2025), [arXiv:2311.07572].
   Study of the local properties of moduli of the Einstein-Yang-Mills theory, which was surprisingly still missing in the liteature, containing a slice theorem and stability results.

3. ∞-Bundles, invited contribution to the Topology Section of the Encyclopedia of Mathematical Physics (second edition), 4:77-97 (2025), arXiv:2308.04196.
   Encyclopedia article on principal ∞-bundles in ∞-topoi, hopefully suitable as an invitation and for getting a first overview of the topic.

4. Lorentzian bordisms in algebraic quantum field theory, with J. MacManus and A. Schenkel, 34 pp., Lett. Math. Phys., 115:16 (2025), [arXiv:2308.01026].
   First step towards comparing the algebraic and bordism-based approaches to QFT, establishing a construction to pass between the pictures and showing that time evolution in both pictures corresponds to each other.

5. Higher geometric structures on manifolds and the gauge theory of Deligne cohomology, with C. S. Shahbazi, 102 pp., arXiv:2304.06633.
   Develops smooth higher symmetry groups of higher geometric structures on manifolds, proves their universal property (that they control equivariant structures), and introduces as mooth moduli stacks of higher geometric structures. Uses this to show that moduli stacks of NSNS supergravity solutions obtained via higher geometry and via generalised geometry are equivalent, even though field configurations are not.

6. An ∞-categorical localisation functor for categories of simplicial diagrams, 27 pp., arXiv:2207.14608.
   An explicit construction of of an ∞-functor establishing the fact that localising categories of simplicial presheaves at objectwise weak homotopy equivalences yields ∞-presheaves; having such a construction explicitly is often very helpful in computations.

7. Gerbes in geometry, field theory, and quantisation, Complex Manifolds 8(1):150-182 (2021), in special volume on Generalized Geometry, [arXiv:2102.10406].
   A introduction and overview of recent developments around bundle gerbes, making links including to functorial field theory, supergravity, differential cohomology and higher versions of symplectic geometry.

8. Principal ∞-bundles and smooth String group models, Mathematische Annalen, 387(1-2):689-743 (2023), [arXiv:2008.12263].
   Proves the conjecture from two papers below that a proposed new string group model is exactly that, and to that end develops further the notion of principal ∞-bundles in ∞-topoi, as well as correcting the definition of what if means to be a smooth model for the string group.

9. The R-local homotopy theory of smooth spaces, J. Homot. Rel. Struc., 17(4):593-650 (2022), [arXiv:2007.06039].
   Detailed study of the homotopy theory obtained by localising simplicial presheaves on cartesian spaces at the real line.

10. Smooth 2-group extensions and symmetries of bundle gerbes, with L. Müller and R. J. Szabo, Comm. Math. Phys. 384(3):1829-1911 (2021), [arXiv:2004.13395].
    Constructs and analyses the smooth 2-group of symmetries of bundle gerbes, proves that this has a universal property cahracterising all equivariant structures on the gerbe, and proposes, among other applications, a new model for the string group.

11. Homotopy sheaves on generalised spaces, Appl. Categ. Struct., 31(49), 57 pp. (2023) , [arXiv:2003.00592].
    A study of descent properties of sheaves of higher categories on smooth spaces more general than manifolds, including, in particular, diffeological spaces.

12. Smooth functorial field theories from B-fields and D-branes, with K. Waldorf, J. Homot. Rel. Struc. 16(1):75-153 (2021), [arXiv:1911.09990].
    The first construction of a smooth functorial field theory on a background manifold, whose bordisms have dimension greater than 1, in this case even an open-closed theory with positive reflection structure.

13. Transgression of D-branes, with K. Waldorf, Adv. Theor. Math. Phys. 25(5):1095-1198 (2021), [arXiv:1808.04894].
    Extends the trangression-regression procedure for bundle gerbes to morphisms between bundle gerbes supported on submanifolds, and thus formalises the duality between these structures on spacetime and how open strings detect them.

14. Geometry and 2-Hilbert space for nonassociative magnetic translations, with L. Müller and R. J. Szabo, Lett. Math. Phys. 109:1827-1866 (2019), [arXiv:1804.08953].
    A higher geometric explanation, in term of 2d parallel transport, of Jackiw's observation that in the presence of magnetic monopoles the translation group of R^n can act non-associatively.

15. Topological insulators and the Kane-Mele invariant: Obstruction and localisation theory, with R. J. Szabo, Rev. Math. Phys. 32(6):2050017, 91 pp. (2020), [arXiv:1712.02991].
    Contains a detailed review of the Kane-Mele invariant of 3d topological insulators and presents three new perspectives on the invariant: via a new version of equivariant de Rham cohomology, via classical homotopy theory, and via equivariant bundle gerbes with connection.

16. Categorical structures on bundle gerbes and higher geometric prequantisation, Ph.D. Thesis, 139 pp., arXiv:1709.06174.
    Develops further the 2-categorical structure of bundle gerbes and their spaces of sections by introducing enriched category theory into this framework.

17. Fluxes, bundle gerbes and 2-Hilbert spaces, with R. J. Szabo, Lett. Math. Phys. 107:1877-1918 (2017), [arXiv:1612.01878].
    Applies the 2-(pre)Hilbert space of sections and developed below in the context of string theory, including explicit examples.

18. The 2-Hilbert space of a prequantum bundle gerbe, with C. Sämann and R. J. Szabo, Rev. Math. Phys., 30:1850001, 101 pp. (2018), [arXiv:1608.08455].
    Develops a 2-(pre)Hilbert space structure on the 2-category of sections of a torsion bundle gerbe and its transgression to the free loop space as a step towards geometric quantisation of 2-plectic 3-forms.

19. A method of deforming G-structures, J. Geom. Phys. 96:72-80 (2015), [arXiv:1410.5849].
    Develops a way to construct new G-structures on a given manifold from old ones, which facilitated the construction of families of 6d instantons in the paper below.

20. Instantons on conical half-flat 6-manifolds, with O. Lechtenfeld, A. Popov, and M. Sperling, JHEP (2015), 030, 38 pp. [arXiv:1409.0030].
    Construction of families of Yang-Mills instantons on a particular class of 6d manifolds.

21. Instantons on sine-cones over Sasakian manifolds, with T. Ivanova, O. Lechtenfeld, A. Popov, and M. Sperling, Phys. Rev. D 90:065028, 10 pp. (2014), [arXiv:1407.2948].
    Construction of Yang-Mills instantons on a particular class of 6d manifolds.

My MSc Thesis on Heterotic Flux Compactifications with Sasakian Manifolds.

You can also find my publications on the ArXiv and Google Scholar.

Recent and upcoming talks

• British Topology Meeting, Cardiff University, September 2025.

• Topology, Geometry, and Physics Seminar Seminar, City University New York (CUNY), 30 May 2025.

• Talk at Signatures and Rough Paths: From Stochastics, Geometry and Algebra to Machine Learning, ICMS Edinburgh, 19--23 May 2025.

• Simons Colloquium on Categorical Symmetries, online colloquium of the eponymous Simons Collaboration, 14 Apr 2025.

• Topology Seminar, EPFL (Lausanne), 02 Apr 2025. Slides.

• Quanum Mathematics Seminar, The University of Nottingham, 04 Dec 2024.