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


Research

Research Interests

Quadratic and hermitian forms, central simple algebras with an involution, real algebra and geometry, non-associative algebras, space-time block codes.

Preprints

(with Vincent Astier) Galois extensions, positive involutions and an application to unitary space-time coding. (arXiv:1809.08954)
(with Vincent Astier) Positive cones and gauges on algebras with involution. (arXiv:1806.05489)
(with Vincent Astier) Positive cones on algebras with involution. (arXiv:1609.06601) [Expanded version of June 2017]

Publications

  1. Positive cones and gauges on algebras with involution
        with Vincent Astier
        Oberwolfach Reports 21 (2018), to appear
        DOI: 10.4171/OWR/2018/21
        (preprint version)
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. Signatures of hermitian forms and applications
        with Vincent Astier
        Oberwolfach Reports 10 (2) (2013), 1853-1856
        DOI: 10.4171/OWR/2013/31
        (preprint version)
  10. 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
  11. 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.]
  12. 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
  13. 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)
  14. 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
  15. Hermitian Morita Theory: a matrix approach
        with David W. Lewis
        Irish Math. Soc. Bull. 62 (2008), 37-41.
        Erratum (updated April 2018)
  16. 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
  17. The hermitian level of composition algebras
        with Susanne Pumplün
        manuscripta mathematica 109 (2002), 511-525.
        DOI: 10.1007/s00229-002-0323-7
  18. 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
  19. 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)
  20. A note on surrogate forms of central simple algebras
        Math. Proc. R. Ir. Acad., 101A(2) (2001), 125-135.
  21. Clifford algebra periodicity for central simple algebras with an involution
        Comm. Algebra, 29(3) (2001), 1141-1152.
        DOI: 10.1081/AGB-100001672
  22. 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)

Book

Specialization of Quadratic and Symmetric Bilinear Forms by Manfred Knebusch (author) and Thomas Unger (translator)

specialization

Springer, Algebra and Applications, Vol. 11
1st Edition., 2010, 188 p., Hardcover
ISBN: 978-1-84882-241-2
Draft Version: PDF.
The original German version Spezialisierung von quadratischen und symmetrischen bilinearen formen can be downloaded here: (link).


Professional Service

Boards/Committees


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




Last updated: 02 October 2018