Chow—Witt Cohomology

• Jens Hornbostel, Matthias Wendt, Heng Xie, MZ.
  The real cycle class map

  Annals of K-Theory 6-2 (2021), 239—317.
  (Longer version available from arXiv.org.)

• Jens Hornbostel, Heng Xie, MZ.
  Chow-Witt rings of split quadrics

  Motivic homotopy theory and refined enumerative geometry, 123—161, Contemp. Math., 745, Amer. Math. Soc., Providence, RI (2020).
  Also available from arxiv.org.

K-Theory and Curvature

• Manuel Amann, David González-Álvaro, MZ.
  Vector bundles of non-negative curvature over cohomogeneity one manifolds
  

  Adv. Math. 405 (2022), Paper No. 108477. Also available from arXiv.org.

• David González-Álvaro, MZ.
  The stable converse soul question for positively curved homogeneous spaces
  

  J. Differential Geom. 119 (2), 261—307 (2021)
  

• David González-Álvaro, MZ.
  Open manifolds with non-homeomorphic positively curved souls
  

  Math. Proc. Camb. Phil. Soc. 169 (2020), 357–376
  The accompanying C++ code for generating Eschenburg spaces and computing their invariants is available from zenodo.

KO-Theory and Witt Rings

• Tobias Hemmert, MZ.
  The Witt rings of many flag varieties are exterior algebras

  Preprint on arXiv.org.

• The γ-filtration on the Witt ring of a scheme
  

  Q. J. Math. 69 (2018), no. 2, 549–583.

• Nilpotence in Milnor-Witt K-Theory
  

  Appendix to: Hornbostel, Jens: Some comments on motivic nilpotence
  Trans. Amer. Math. Soc. 370 (2018), 3001–3015

• Symmetric representation rings are λ-rings
  

  New York J. Math. 21 (2015), 1055–1092.

• KO-Rings of Full Flag Varieties
  

  Trans. Amer. Math. Soc. 367 (2015), 2997–3016.

• Witt Groups of Curves and Surfaces
  

  Math. Zeits. 278 (2014), no. 1–2, 191–227.

• Twisted Witt Groups of Flag Varieties
  

  J. K-Theory 14 (2014), no. 1, 139–184.

• Witt Groups of Complex Cellular Varieties
  

  Documenta Math. 16 (2011), 465–511.

• Witt Groups of Complex Varieties
  

  PhD thesis (2011). Also available from DSpace@Cambridge.

• Comparing Grothendieck-Witt Groups of a Complex Variety to its Real Topological K-Groups
  

  Smith-Knight/Rayleigh-Knight Prize Essay (2009). Also available from DSpace@Cambridge.

Topological Data Analysis

• Alexander Jakubowski, Milica Gasic, MZ.
  Topology of Word Embeddings: Singularities Reflect Polysemy
  

  Proceedings of the Ninth Joint Conference on Lexical and Computational Semantics (*SEM 2020), 103—113, Association for Computational Linguistics (2020). Best Paper Award

Other directions

• Dual involutions in Coxeter groups

  Preprint on arXiv.org.