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Associate Professor in Mathematics
School of Mathematics and Statistics
University College Dublin


Contact Address


School of Mathematics and Statistics
University College Dublin
Belfield
Dublin 4
Ireland

Email: thomas · unger © ucd · ie
Phone: +353-1-716 2586
Fax: + 353-1-716 1172
UCD Researchers page: click here

Office: Room S1.75, Science Centre South, 1st Floor


Public Key


OpenPGP key: download here
Fingerprint: FA00 1562 0C84 0633 9B4C 5CB0 D4E5 D2A9 5567 F2C6


Research

Research Interests

Quadratic and hermitian forms, algebras with involution, (noncommutative) real algebra and geometry, space-time block codes.

Preprint

  • (with Vincent Astier) Hermitian Sylvester and Pfister theorems for Azumaya algebras with involution. arXiv:2210.04851

Publications

  1. The life and work of David W. Lewis (1944-2021)
        Irish Math. Soc. Bull. 82 (2022), 5-16
        DOI: 10.33232/BIMS.0089.5.16
  2. Positive cones and gauges on algebras with involution
        with Vincent Astier
        International Mathematics Research Notices, Volume 2022, Issue 10 (2022), 7259-7303
        DOI: 10.1093/imrn/rnaa337
        Preprint version: arXiv:1806.05489
  3. Positive cones on algebras with involution
        with Vincent Astier
        Adv. Math. 361 (2020), 106954, 1-48
        DOI: 10.1016/j.aim.2019.106954
        Preprint version: arXiv:1609.06601
  4. Galois extensions, positive involutions and an application to unitary space-time coding
        with Vincent Astier
        Adv. Math. Commun. 13 (3) (2019), 513-516
        DOI: 10.3934/amc.2019032
        Preprint version: arXiv:1809.08954
  5. Positive cones and gauges on algebras with involution
        with Vincent Astier
        Oberwolfach Reports 15 (2) (2018), 1253-1255
        DOI: 10.4171/OWR/2018/21
        (preprint version)
  6. Signatures of hermitian forms, positivity, and an answer to a question of Procesi and Schacher
        with Vincent Astier
        J. Algebra 508 (2018), 339-363
        DOI: 10.1016/j.jalgebra.2018.05.004
        Preprint version: arXiv:1511.06330
  7. Signatures, sums of hermitian squares and positive cones on algebras with involution
        with Vincent Astier
        Electron. Res. Announc. Math. Sci. 25 (2018), 16-26
        DOI: 10.3934/era.2018.25.003
        Preprint version: arXiv:1706.01264
  8. Weakly hyperbolic involutions
        with Karim Johannes Becher
        Expo. Math. 36 (2018), 78-97
        DOI: 10.1016/j.exmath.2017.08.006
        Preprint version: arXiv:1207.4658
  9. Stability index for algebras with involution
        with Vincent Astier
        Contemporary Mathematics 697 (2017), 41-50
        DOI: 10.1090/conm/697/14045
        Preprint version: arXiv:1406.5892
  10. Algebraic structures for capturing the provenance of SPARQL queries
        with Floris Geerts, Grigoris Karvounarakis, Irini Fundulaki, Vassilis Christophides
        Journal of the ACM, Vol. 63, No. 1, Article 7 (2016), 7:1-7:63
        DOI: 10.1145/2810037
  11. Signatures of hermitian forms and "prime ideals" of Witt groups
        with Vincent Astier
        Adv. Math. 285 (2015), 497-514
        DOI: 10.1016/j.aim.2015.07.035
        Preprint version: arXiv:1303.3494
  12. Signatures of hermitian forms and the Knebusch Trace Formula
        with Vincent Astier
        Math. Annalen 358 (3-4) (2014), 925-947
        DOI: 10.1007/s00208-013-0977-3
        Preprint version (= final version plus erratum): arXiv:1003.0956
  13. Signatures of hermitian forms and applications
        with Vincent Astier
        Oberwolfach Reports 10 (2) (2013), 1853-1856
        DOI: 10.4171/OWR/2013/31
        (preprint version)
  14. Space-time block codes from nonassociative division algebras
        with Susanne Pumplün
        Adv. Math. Commun. 5 (3) (2011), 449-471
        DOI: 10.3934/amc.2011.5.449
        Preprint version: arXiv:1006.2348
  15. Quadratic forms and space-time block codes from generalized quaternion and biquaternion algebras
        with Nadya Markin
        IEEE Trans. Inf. Theory 57 (9) (2011), 6148-6156
        DOI: 10.1109/TIT.2011.2161909
        Preprint version: arXiv:0807.0199
        [Annoying typo: in equation (4), x should be replaced by j.]
  16. The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution
        with Igor Klep
        J. Algebra 324 (2010), 256-268
        DOI: 10.1016/j.jalgebra.2010.03.022
        Preprint version: arXiv:0810.5254
  17. The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution
        with Igor Klep
        Oberwolfach Reports 6 (2) (2009), 1388-1390
        DOI: 10.4171/OWR/2009/25
        (preprint version)
  18. A hermitian analogue of the Bröcker-Prestel theorem
        with Vincent Astier
        Indagationes Mathematicae (N.S.) 19 (3) (2008), 349-358
        DOI: 10.1016/S0019-3577(09)00007-X
  19. Hermitian Morita Theory: a matrix approach
        with David W. Lewis
        Irish Math. Soc. Bull. 62 (2008), 37-41.
        Erratum (updated April 2018)
  20. The Hasse principle for similarity of hermitian forms
        with David W. Lewis and Jan Van Geel
        J. Algebra 285 (2005), 196-212.
        DOI: 10.1016/j.jalgebra.2004.12.002
  21. The hermitian level of composition algebras
        with Susanne Pumplün
        manuscripta mathematica 109 (2002), 511-525.
        DOI: 10.1007/s00229-002-0323-7
  22. A local-global principle for algebras with involution and hermitian forms
        with David W. Lewis
        Math. Zeit. 244 (2003), 469-477.
        DOI: 10.1007/s00209-003-0490-6,
        Erratum
  23. A weak Hasse principle for central simple algebras with an involution
        with David W. Lewis and Claus Scheiderer
        Doc. Math. Extra Volume, Proc. Conf. Quadratic Forms and Related Topics, Baton
        Rouge, La., 2001, 241-251 (2001)
  24. A note on surrogate forms of central simple algebras
        Math. Proc. R. Ir. Acad., 101A(2) (2001), 125-135.
  25. Clifford algebra periodicity for central simple algebras with an involution
        Comm. Algebra, 29(3) (2001), 1141-1152.
        DOI: 10.1081/AGB-100001672
  26. Genetic Algorithms: a survey of some mathematical models --- Part I
        Irish Math. Soc. Bull. 41 (1998), 57-71.

Not Peer Reviewed

  • Signatures, sums of hermitian squares and positive cones on algebras with involution
        with Vincent Astier
        Séminaire de Structures Algébriques Ordonnées 2015-2016, 91 (2017)
  • Signatures of hermitian forms, prime ideals and morphisms
        with Vincent Astier
        Séminaire de Structures Algébriques Ordonnées 2012-2013, 89 (2014)

Books

  • Real Algebra: A First Course by Manfred Knebusch and Claus Scheiderer
    Translated and with contributions by Thomas Unger

    Universitext, Springer Nature, 2022
    DOI: 10.1007/978-3-031-09800-0
    (Revised and updated English translation of Einführung in die reelle Algebra.)

    specialization

  • Specialization of Quadratic and Symmetric Bilinear Forms by Manfred Knebusch
    Translated by Thomas Unger

    Algebra and Applications, Vol. 11, Springer, 2010
    DOI: 10.1007/978-1-84882-242-9
    The original German version Spezialisierung von quadratischen und symmetrisch bilinearen Formen can be downloaded here: (link).

    specialization



Professional Service

Boards/Committees


Conferences Co-organized (as local and/or scientific organizer)




Last updated: 26 October 2022