Thomas Unger

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

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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

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Public Key

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

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Research

Research Interests

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

Preprint

• (with Vincent Astier) Pfister's local-global principle 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 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).
  
  

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Professional Service

Boards/Committees

• Editorial Board, Bulletin of the Irish Mathematical Society
• Editorial Board, Encyclopedia of Mathematics
• Member (2013-2016), Electronic Publishing Committee, European Mathematical Society

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

• Representations and Finite Fields: Conference in honour of Professor Rod Gow, UCD, Dublin, May 28, 2013.
• The Lewisfest, UCD, Dublin, July 23-24, 2009.
• Workshop on K-Theory, Algebraic Groups and Related Structures, UCD, Dublin, July 5-8, 2004.
• Conference on K-Theory and Linear Algebraic Groups, Gerhard Mercator University, Duisburg, September 9-15, 2001.
• QF99 - Quadratic Forms and Their Applications, UCD, Dublin, July 5-9, 1999

Last updated: 19 April 2023