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Research interests:
My research is in pure mathematics, but it is usually motivated by problems in physics or other applications.
To me, such problems are a great guiding principle for where to look for new mathematics. More concretely, my main interests are:
- Field theories and higher geometry:
relations between field theories on target spaces and higher geometric structures,
links between different perspectives on field theories,
geometry on generalisations of manifolds.
- Applications to physics: Topological phases, quantum field theory, string theory.
Publications and Preprints
- Gerbes in Geometry, Field Theory, and Quantisation, arXiv:2102.10406.
- Principal ∞-Bundles and Smooth String Group Models, arXiv:2008.12263.
- The R-Local Homotopy Theory of Smooth Spaces, arXiv:2007.06039.
- Smooth 2-Group Extensions and Symmetries of Bundle Gerbes, with Lukas Müller and Richard J. Szabo, arXiv:2004.13395.
- Sheaves of Higher Categories and Presentations of Smooth Field Theories, arXiv:2003.00592.
- Smooth Functorial Field Theories from B-Fields and D-Branes, with Konrad Waldorf, J. Homot. Rel. Str. 16(1):75-153 (2021), [arXiv:1911.09990].
- Transgression of D-Branes, with Konrad Waldorf, arXiv:1808.04894.
- Geometry and 2-Hilbert Space for Nonassociative Magnetic Translations, with Lukas Müller and Richard J. Szabo, Lett. Math. Phys. 109:1827-1866 (2019), [arXiv:1804.08953].
- Topological Insulators and the Kane-Mele Invariant: Obstruction and Localisation Theory, with Richard J. Szabo, Rev. Math. Phys. 32(6):2050017, 91 pp. (2020), [arXiv:1712.02991].
- Categorical Structures on Bundle Gerbes and Higher Geometric Prequantisation, Ph.D. Thesis, arXiv:1709.06174.
- Fluxes, bundle gerbes and 2-Hilbert spaces, with Richard J. Szabo, Lett. Math. Phys. 107:1877-1918 (2017), [arXiv:1612.01878].
- The 2-Hilbert space of a prequantum bundle gerbe, with Christian Sämann and Richard J. Szabo, Rev. Math. Phys., 30:1850001, 101 pp. (2018), [arXiv:1608.08455].
- A method of deforming G-structures, J. Geom. Phys. 96:72-80 (2015), [arXiv:1410.5849].
- Instantons on conical half-flat 6-manifolds, with Olaf Lechtenfeld, Alexander Popov, and Marcus Sperling, JHEP (2015), 030, 38 pp. [arXiv:1409.0030].
- Instantons on sine-cones over Sasakian manifolds, with Tatiana Ivanova, Olaf Lechtenfeld, Alexander Popov, and Marcus Sperling, Phys. Rev. D 90:065028, 10 pp. (2014), [arXiv:1407.2948].
See also
Google Scholar or
Inspirehep.
MSc Thesis
Recent and upcoming talks
- 24/02/21, University of Aberdeen; Algebra Seminar.
- 23/02/21, University of Warwick; Algebraic Topology Seminar.
- 29/01/21, Instituto Superior Técnico, Lisbon; TQFT Seminar.
- 24/11/20, Universität des Saarlandes; Algebra and Number Theory Seminar.
- 28/10/20, City University of New York; Topology, Geometry, and Physics Seminar.
- 15/10/20, University of Manchester; Geometry, Topology and Mathematical Physics Seminar.
- 13/10/20, University of Leeds; Algebra Seminar.
- 22/09/20, University of Surrey; Fields, Strings and Geometry Seminar.
- 15/06/20, University of Oxford; Topology Seminar.
- 23/03/20, Queen Mary University, London; String Theory Seminar - cancelled due to corona outbreak.
- 04/03/20, Conference Generalized Geometry and Applications, Hamburg.
- 13/02/20, University of Sheffield; Topology Seminar.
- 11/02/20, University of Liverpool; String Phenomenology Seminar.
- 21/01/20, University of Montpellier; Derived and Higher Algebraic Geometry Seminar.
Notes
- Levin-Wen Models, ZMP Seminar, Hamburg, 11/06/20.
- Higher Topoi and Hypercoverings, Higher Structures Research Seminar, Hamburg, 16/12/19.
- Derived Deformation Theory - An Introduction, Higher Structures Research Seminar, Hamburg, 14/10/19.
- Little Cubes and Manifold Topology, Higher Structures Research Seminar, Hamburg 13/05/19.
- Operads and their Algebras, ZMP Seminar Hamburg, 15/11/18.
- Topological Insulators and the Kane-Mele Invariant, MPIM Bonn, 24/10/18.