Chow—Witt Cohomology
- Jens Hornbostel, Matthias Wendt, Heng Xie, MZ.
The real cycle class mapAnnals of K-Theory 6-2 (2021), 239—317.
(Longer version available from arxiv.org.) - Jens Hornbostel, Heng Xie, MZ.
Chow-Witt rings of split quadricsMotivic 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
- 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
- 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 - Tobias Hemmert, MZ.
The Witt rings of many flag varieties are exterior algebras - 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
- KO-Rings of Full Flag Varieties
- Witt Groups of Curves and Surfaces
- Twisted Witt Groups of Flag Varieties
- 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
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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
Accepted as a long paper to the SIGdial 2024 Conference. Preprint on arxiv.org.
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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 SIGdial 2022 Conference, 564—581, Association for Computational Linguistics.
- 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.