I am an Assitant (Akademischer Rat auf Zeit) in the Topology group at the University of Münster; until recently, I was part of the Topology group at the University of Bonn.
During spring 2022 I visited the Mittag-Leffler-Institute, Stockholm, as part of the program Higher algebraic structures in algebra, topology and geometry, and towards the end of 2022 I will move to the University of Aberdeen as lecturer.
Mathematisches Institut |
48149 Münster, Germany
|Office: ||505 |
|e-mail: || firstname.lastname@example.org |
|Office hours: || by appointment ||
Algebraic & geometric Topology, homotopical Algebra and more specifically: The homotopy theory of diffeomorphism groups and cobordism categories, and their relation to algebraic K- and L-theory, parametrised homotopy theory and its relation to operator algebras and positive scalar curvature
Preprints and Publications
- with A.Lachmann & W.Steimle: The localisation theorem for algebraic K-theory of stable categories.
arXiv:2205.06104 (26 pages, 2022, in revision)
- with R.Haugseng, S.Linskens & J.Nuiten: Two-variable fibrations, factorisation systems and categories of spans.
arXiv:2011.11042 (59 pages, 2022, submitted)
- with R.Haugseng, S.Linskens & J.Nuiten: Lax monoidal adjunctions, two-variable fibrations and the calculus of mates.
arXiv:2011.08808 (51 pages, 2021, submitted)
- with G.Heuts & J.Ruit: A short proof of the straightening theorem.
arXiv:2111.00069 (41 pages, 2021, submitted)
- with W.Steimle: Stable moduli spaces of hermitian forms.
arXiv:2103.13911 (with an appendix by Y.Harpaz, 94 pages, 2021, submitted)
- with A.Krause: Mapping spaces in coherent nerves.
arXiv:2011.09345 (14 pages, 2020)
- with B.Calmès, E.Dotto, Y.Harpaz, M.Land, K.Moi, D.Nardin, T.Nikolaus & W.Steimle: Hermitian K-Theory for stable ∞-categories III: Grothendieck-Witt groups of rings.
arXiv:2009.07225 (63 pages, 2020, in revision)
- with B.Calmès, E.Dotto, Y.Harpaz, M.Land, K.Moi, D.Nardin, T.Nikolaus & W.Steimle: Hermitian K-Theory for stable ∞-categories II: Cobordism categories and Additivity.
arXiv:2009.07224 (159 pages, 2020, in revision)
- with B.Calmès, E.Dotto, Y.Harpaz, M.Land, K.Moi, D.Nardin, T.Nikolaus & W.Steimle: Hermitian K-Theory for stable ∞-categories I: Foundations.
Selecta Mathematica, vol. 29, no. 1 (2023), article no. 10, 269 pages
- with M.Land & T.Nikolaus: On the homotopy type of L-spectra of the integers.
Journal of Topology, vol. 14, no. 1 (2021), pp. 183-214, Erratum
- with I.Bokor, D.Crowley, S.Friedl, D.Kasprowski, M.Land & J.Nicholson: Connected sum decompositions of high-dimensional manifolds.
Matrix Annals, vol. 4 (2021), pp. 5-30
- with S.Sagave: Homotopical and operator algebraic twisted K-theory.
Mathematische Annalen, vol. 378 (2020), pp. 1021-1059
- with C.Schlichtkrull & S.Sagave: Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces.
Forum of Mathematics Sigma, vol. 8 (2020), article no. e16, 84 pages
- with M.Land, W.Lück & O.Randal-Williams: A vanishing theorem for tautological classes of aspherical manifolds.
Geometry & Topology, vol. 25 (2021), pp. 47-110
- with N.Perlmutter: Cobordism categories and moduli spaces of odd dimensional manifolds.
Advances in Mathematics, vol. 353, no. 7 (2019), pp. 526-590
- with M.Joachim: Twisted Spin cobordism and positive scalar curvature.
Journal of Topology, vol. 13, no. 1 (2020), pp. 1-58
- with S.Büscher, O.Röndigs & M.Stelzer: The Goodwillie Spectral Sequence for iterated loopspaces and topological realisation at odd primes.
Algebraic and Geometric Topology, vol. 13, no. 1 (2013), pp. 127-169
- Parametrised algebraic surgery.
Oberwolfach Reports vol. 17, no. 2-3, Workshop: Topologie (2020), pp. 1116-1121
- Algebraic Cobordism categories and Grothendieck-Witt theory.
Oberwolfach Reports vol. 17, no. 1, Workshop: Manifolds and Groups (2020), pp. 437-440
- The Tate Diagonal.
Oberwolfach Reports vol. 15, no. 1, Arbeitsgemeinschaft: Topological Cyclic Homology (2018), pp. 825-838
- Twisted Spin Cobordism.
Oberwolfach Reports vol. 11, no. 3, Workshop: Analysis, Geometry and Topology of positive scalar curvature (2014), pp. 2013-2014
In the summer term I will teach a coure on higher categories and their uses in algebraic topology and homological algebra, Higher Categories II
Some lecture notes: