Research

Research

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.

Topological K-Theory and Curvature

• An extension of Steinberg's Theorem to biquotient pairs of subgroups

  Preprint on arxiv.org.

• 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, Hermitian K-theory and Witt Rings

• Jens Hornbostel, Herman Rohrbach, MZ.
  Atiyah-Segal completion for the Hermitian K-theory of Symplectic Groups

  Accepted for publication in Algebraic & Geometric Topology. Preprint on arxiv.org.

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

  Trans. Amer. Math. Soc., vol. 377, no. 9 (2024), 6427–6463.

• 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

• Benjamin Matthias Ruppik, Michael Heck, Carel van Niekerk, Renato Vukovic, Hsien-chin Lin, Shutong Feng, MZ, Milica Gašić.
  Local Topology Measures of Contextual Language Model Latent Spaces With Applications to Dialogue Term Extraction
  

  Proceedings of the 25th Annual Meeting of the Special Interest Group on Discourse and Dialogue (SigDIAL 2024), 344--356, Association for Computational Linguistics (2024)

• Renato Vukovic, Michael Heck, Benjamin Ruppik, Carel van Niekerk, MZ, Milica Gašic.
  Dialogue Term Extraction using Transfer Learning and Topological Data Analysis
  

  Proceedings of the 23rd Annual Meeting of the Special Interest Group on Discourse and Dialogue (SigDIAL 2022), 564--581, Association for Computational Linguistics (2022)

• 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. Best Paper Award

Other directions

• Dual involutions in Coxeter groups

  Communications in Algebra, 52:3 (2024), 1028–1037.
  Author’s original manuscript available from arxiv.org.