## Research interests

I am an algebraic topologist with a special interest in the spectrum of topological modular forms *TMF*. I am also interested in several related

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:

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)

## Preprints and Publications

Rings of modular forms and a splitting of TMF_{0}(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 C_{2}-spectrum Tmf_{1}(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)
## Other Documents and Non-arXived Preprints

## Theses

## Talks

### 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.

### Students

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!