Fabian Hebestreit

Since January I am a Professor at the Universität Bielefeld. 

Until recently, I was a lecturer in the Department of Mathematics at the University of Aberdeen, before that a member the Topology group at WWU Münster and even before that I obtained my Habilitation in the Topology group of the RFWU Bonn, advised by Wolfgang Lück. 

Research interests

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; higher categories as foundations for the above.

Publications and Preprints

Category theory

• with J.Steinebrunner: A short proof that Rezk's nerve is fully faithful.

arXiv: 2312.09889 (12 pages, 2023, submitted)

• with R.Haugseng, S.Linskens & J.Nuiten: Two-variable fibrations, factorisation systems and categories of spans.
  Forum of Mathematics Sigma, vol. 11 (2023), article no. e111, 70 pages

• with R.Haugseng, S.Linskens & J.Nuiten: Lax monoidal adjunctions, two-variable fibrations and the calculus of mates.
  Proceedings of the London Mathematical Society, vol. 127, no. 4 (2023), pp. 889-957

• with G.Heuts & J.Ruit: A short proof of the straightening theorem.
  arXiv: 2111.00069 (41 pages, 2021, submitted)

• with A.Krause: Mapping spaces in coherent nerves.
  arXiv: 2011.09345 (14 pages, 2020)

Algebraic and hermitian K-theory

• with A.Krause & M.Ramzi: A note on quadratic forms.

Bulletin of the London Mathematical Society, vol. 56, no. 5 (2024), pp. 1803-1818

• with A.Lachmann & W.Steimle: The localisation theorem for algebraic K-theory of stable categories.
  to appear in Proceedings of the Royal Society of Edinburgh (37 pages, 2023, available here)

• with W.Steimle: Stable moduli spaces of hermitian forms.
  arXiv: 2103.13911 (with an appendix by Y.Harpaz, 94 pages, 2021, submitted)

• 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

Algebraic and geometric Topology

• 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

Other writing

• with M.Land: Apprenticeship with an algebraic surgeon.

Celebratio Mathematica, Ranicki memorial issue (2022)

• with M.Land & T.Nikolaus: The initial quadratic form on an abelian group.

• 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

Teaching

During the summer term '24 I will teach Linear Algebra I and Higher categories and Algebraic K-theory I.

Some lecture notes on Algebraic Topology, Higher Categories and Algberaic K-Theory are here.