I am an algebraic topologist with a special interest in the spectrum of topological modular forms TMF. I am also interested in several related Understanding torus-equivariant TMF (joint with D. Gepner and T. Nikolaus)
Towards the Brauer group of TMF (joint with B. Antieau and V. Stojanoska)
Unstable periodic homotopy theory (joint with G. Heuts)
Stacks associated with connective tmf with level structures (joint with V. Ozornova)
Galois theory in equivariant context (joint with M. Kedziorek and V. Ozornova)
Periodic localizations of algebraic K-theory (M. Land and G. Tamme)
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. This includes the following collaborations:
Preprints and Publications
Rings of modular forms and a splitting of TMF0(7) (joint with Viktoriya Ozornova)
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), 425-456. (arXiv)
Hilbert Manifolds, Bulletin of the Manifold Atlas (2014, expository)
Spectral Sequences in String Topology, Algebraic & Geometric Topology 11 (2011), 2829-2860. (arXiv)
Lecture notes and expository writing
Academic Year 2018/19
Block 3, Topologie en Meetkunde
Spring, Mastermath Algebraic Topology II (jointly with Gijs Heuts)
Spring, Master seminar on a rational homotopy theory (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!