Research

Publications

• With T. Unger: Hermitian Sylvester and Pfister theorems for Azumaya algebras with involution. Submitted. Preprint version: arXiv:2210.04851
• With T. Unger: Positive cones and gauges on algebras with involution. International Mathematics Research Notices, published on-line 30/12/2020, 1-45 DOI: 10.1093/imrn/rnaa337 Preprint version: arXiv:1806.05489
• With T. Unger: Positive cones on algebras with involution. Adv. Math. 361 (2020), 106954, 1-48. DOI: 10.1016/j.aim.2019.106954. Preprint: arXiv:1609.06601.
• With T. Unger: Galois extensions, positive involutions and an application to unitary space-time coding. Advances in Mathematics of Communications 13 (3) (2019), 513-516. DOI: 10.3934/amc.2019032. Preprint: arXiv:1809.08954.
• With T. Unger: Positive cones and gauges on algebras with involution, Oberwolfach Reports 15 (2) (2018), 1253-1255 DOI: 10.4171/OWR/2018/21. Preprint.
• With T. Unger: Signatures of hermitian forms, positivity, and an answer to a question of Procesi and Schacher, Journal of Algebra 508 (2018), 339-363. Preprint version: arXiv:1511.06330.
• With T. Unger: Signatures, sums of hermitian squares and positive cones on algebras with involution, Electronic Research Announcements in Mathematical Sciences 28 (2018), 16-26. arXiv:1706.01264 (expository article).
• With T. Unger: Stability index for algebras with involution, Contemporary Mathematics 697 (2017), 41-50. arXiv:1406.5892.
• With T. Unger: Signatures of hermitian forms and "prime ideals" of Witt groups, Advances in Mathematics 285 (2015), 497-514.
  Preprint version: arXiv:1303.3494
• With T. Unger: Signatures of hermitian forms and the Knebusch trace formula (preprint version, arXiv), Mathematische Annalen, 358 (3-4), 2014.
• With T. Unger: Signatures of hermitian forms and applications (preprint version), Oberwolfach Reports 10 (2013).
• Elementary equivalence of lattices of open sets definable in o-minimal expansions of fields (preprint version), Fundamenta Mathematicae, 220(1), 2013.
• With H. Mariano: Realising profinite reduced special groups (preprint version), Pacific Journal of Mathematics, 250(2), 2011.
• With T. Unger: A hermitian analogue of the Bröcker-Prestel theorem (preprint version), Indagationes Mathematicae 19(3), 2008.
• Generic splitting for special groups (preprint version), Journal of Algebra 320(4), 2008.
• Elementary equivalence of some rings of definable functions (preprint version), Archive for Mathematical Logic 47(4), 2008.
• Special groups whose isometry relation is a finite union of cosets (preprint version), Journal of Symbolic Logic 73(2), 2008.
  (New version, correcting the old --and false-- proposition 1.2 and its consequences.)
• On some sheaves of reduced special groups (preprint version), Archive for Mathematical Logic 46(5-6), 2007.
• With S. Pumplün: Nonassociative quaternion algebras over rings (preprint version), Israel Journal of Mathematics 155, 2006.
• With M. Tressl: Axiomatization of local-global principles for pp-formulas in spaces of orderings (preprint version), Archive for Mathematical Logic 44(1), 2005.
• Pfister's subform theorem for reduced special groups (preprint version), Journal of Pure and Applied Algebra 189(1-3), 2004.
• Some model-theoretic results in the algebraic theory of quadratic forms (preprint version), Annals of Pure and Applied Logic 112(2-3), 2001.
  (Corrected version: lemma 4.4 was false in the first one.)
• Quelques propriétés modèles-théoriques des groupes spéciaux réduits, C. R. Acad. Sci. 326(4), 1998.

Notes

• A “cell“ decomposition in O-minimal structures that is independent of a permutation of the coordinates.
• An explicit weak product of special groups.