Thomas Unger

Lecturer in Mathematics
School of Mathematical Sciences
University College Dublin
PhD (NUI), 2001

Contact Address

School of Mathematical Sciences
University College Dublin
Belfield
Dublin 4
Ireland

Email: thomas · unger © ucd · ie
Phone: +353-1-716 5768
Fax: + 353-1-716 1172
Official Web page: click here

Office: Room 3.53, Belfield Office Park 9/10 ("NexusUCD"), 3rd Floor
Location map: http://g.co/maps/s6ffs

Research

Research Interests

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

Preprints

(with Vincent Astier) Signatures of hermitian forms and "prime ideals" of Witt groups. (arXiv:1303.3494)
(with Karim Johannes Becher) Weakly hyperbolic involutions. (arXiv:1207.4658)
(with Vincent Astier) Signatures of hermitian forms and the Knebusch Trace Formula. (arXiv:1003.0956)

Publications

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
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
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
The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution
    with Igor Klep
    Oberwolfach Reports 6 (2) (2009), 1388-1390
    (preprint version)
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
Hermitian Morita Theory: a matrix approach
with David W. Lewis
Irish Math. Soc. Bull. 62 (2008), 37-41.
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
The hermitian level of composition algebras
    with Susanne Pumplün
    manuscripta mathematica 109 (2002), 511-525.
    DOI: 10.1007/s00229-002-0323-7
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 .
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)
A note on surrogate forms of central simple algebras
Math. Proc. R. Ir. Acad., 101A(2) (2001), 125-135.
Clifford algebra periodicity for central simple algebras with an involution
Comm. Algebra, 29(3) (2001), 1141-1152.
DOI: 10.1081/AGB-100001672
Genetic Algorithms: a survey of some mathematical models --- Part I
Irish Math. Soc. Bull. 41 (1998), 57-71.

Book

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

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).

Teaching

Academic Year 2012 - 2013

Semester 1
MATH 10270 Linear Algebra in the Mathematical Sciences
Semester 2
MATH 30030 Advanced Linear Algebra

Professional Service

Boards/Committees

Editorial Board, Encyclopedia of Mathematics
Member, 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

Student Supervision

James O’Shea: MSc (2003), Hermitian Levels of Octonion Algebras
Lien Boelaert: MSc (2009), Cyclicity of Central Simple Algebras and the Linear Algebraic Group E_8 (jointly supervised with J. Van Geel -- Ghent University)
James O’Shea: PhD (2007), Levels and Sublevels of Composition Algebras
Ronan Flatley: PhD (2011), Symbol Algebras, Involutions and Trace Forms (jointly supervised with D. Lewis)

Last updated: 30 May 2013