I am an algebraic topologist with a special interest in the spectrum of topological modular forms TMF. I am also interested in several related A splitting for TMF0(7) (joint with V. Ozornova)
Understanding torus-equivariant TMF (joint with D. Gepner and T. Nikolaus)
and unrelated questions in abstract homotopy theory, stable and unstable chromatic homotopy theory and (derived) algebraic geometry.
Currently I am thinking mostly about the Bousfield-Kuhn functor, TMF with level structures, equivariant TMF and its applications to elliptic
genera and Brauer groups of moduli stacks of elliptic curves. This includes the following collaborations:
Preprints and Publications
A Whitehead theorem for periodic homotopy groups, arXiv:1811.04030 (joint with Tobias Barthel and Gijs Heuts)
Topological modular forms with level structures: decompositions and duality, arXiv:1806.06709
Decomposition results for rings of modular forms, arXiv:1710.03461
Monadicity of the Bousfield-Kuhn functor, arXiv:1707.05986 (joint with Rosona Eldred, Gijs Heuts and Akhil Mathew)
The Brauer group of the moduli stack of elliptic curves, arXiv:1608.00851 (joint with Ben Antieau)
Gorenstein duality for Real spectra (joint with John Greenlees), Algebraic & Geometric Topology 17 (2017), 3547-3619 , Erratum to the published version
Appendix B: 'Descent for higher real K-theories'
to 'Descent in algebraic K-theory and a conjecture of Ausoni-Rognes', arXiv:1606.03328
(joint with Niko Naumann and Justin Noel, 2016)
The C2-spectrum Tmf1(3) and its invertible modules (joint with Mike Hill), Algebraic & Geometric Topology 17 (2017) 1953-2011 (arXiv)
Fibration Categories are Fibrant Relative Categories, arXiv:1503.02036 , Algebraic & Geometric Topology 16 (2016), 3271-3300. (arXiv)
Fibrancy of Partial Model Categories (joint with Viktoriya Ozornova, 2015) Homology, Homotopy and Appl Volume 17.2 (2015), 53-80 (arXiv)
Affineness and Chromatic Homotopy Theory (joint with Akhil Mathew) J Topology (2015) 8 (2): 476-528 (arXiv, Erratum to the published version)
Vector Bundles on the Moduli Stack of Elliptic Curves, Journal of Algebra Volume 428 (2015), 425â€“456. (arXiv)
Hilbert Manifolds, Bulletin of the Manifold Atlas (2014, expository)
Spectral Sequences in String Topology, Algebraic & Geometric Topology 11 (2011), 2829-2860. (arXiv)
Other Documents and Non-arXived Preprints
Academic Year 2018/19
Block 3, Topologie en Meetkunde
Spring, Mastermath Algebraic Topology II (jointly with Gijs Heuts)
Spring, Master seminar on a topic in algebraic topology (jointly with Gijs Heuts)
Academic Year 2017/18
Block 3, Topologie en Meetkunde
Spring, Master seminar seminar on topological K-theory (jointly with Gijs Heuts)
Previously, courses at the University of Virginia and the University of Bonn on linear algebra, multivariable calculus, algebra, homology theories and elliptic cohomology
Currently I supervise the master theses of Joost van Geffen, Jorge Becerra and Jeroen van der Meer and the PhD thesis of Jack Davies.
I supervised the master thesis of Simone Fabbrizzi in Bonn on the computation of Brauer groups of moduli stacks of elliptic curves
I supervised three bachelor theses so far on the topics de Rham cohomology, homology with local coefficients and genus formulae of modular curves. Generally I am happy to supervise bachelor theses in topology or on topics related to modular forms or elliptic curves.
If you are student interested in a thesis or reading project, please contact me!