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Researchers at UCD

researcher

Thomas Unger

Associate Professor

School of Mathematics & Statistics
Room S1.75, Science Centre South, 1st Floor
Belfield, Dublin 4, Ireland

Tel: +353-1-716 2586
Email: thomas.unger@ucd.ie

Professional

         

Conference Contributions

Unger, T. (2014) Signaturen von hermiteschen Formen und Anwendungen. [Invited Lecture], Akademische Feier zum 75. Geburtstag von Professor Manfred Knebusch, University of Regensburg , 08-FEB-14 - 08-FEB-14.
Unger, T. (2013) [Conference Organising Committee Chairperson], Representations and Finite Fields: Conference in honour of Professor Rod Gow, UCD, Dublin , 28-MAY-13 - 28-MAY-13.
Unger, T. (2013) Signatures of hermitian forms and applications. [Invited Lecture], Quadratic Forms and Linear Algebraic Groups, Mathematische Forschungsinstitut Oberwolfach, Germany , 16-JUN-13 - 22-JUN-13.
Unger, T. (2013) Signatures of hermitian forms, Knebusch trace formula and prime ideals of Witt groups. [Invited Lecture], International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms, Puerto Natales, Patagonia, Chile , 16-DEC-13 - 21-DEC-13.
Unger, T.; (2010) Signatures of hermitian forms. [Invited Lecture], 9th Colloquiumfest on Algebra and Logic, Bukowina Tatrzanska , 21-JUN-10 - 24-JUN-10.
Unger, T; (2009) The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution. [Invited Lecture], Quadratic Forms and Linear Algebraic Groups, Mathematische Forschungsinstitut Oberwolfach, Germany , 10-MAY-09 - 16-MAY-09.
Unger, T. (2009) [Conference Organising Committee Chairperson], The Lewisfest, Conference in honour of Professor David Lewis on the occasion of his 65th birthday, UCD, Dublin , 23-JUL-09 - 24-JUL-09.
Unger, T; (2008) Towards a reduced theory of hermitian forms. [Invited Lecture], 5th Linear Algebra Workshop, Kranjska Gora, Slovenia , 27-MAY-08 - 05-JUN-08.

Committees

Committee : Editorial Board Member, Encyclopedia of Mathematics
Committee : Editorial Board Member, Bulletin of the Irish Mathematical Society
Committee : Member, Electronic Publishing Committee, European Mathematical Society
             

Publications

Books

Knebusch, M. (Author) and Unger, T. (Translator); (2010) Specialization of Quadratic and Symmetric Bilinear Forms. London: Springer. [Details]
   

Peer Reviewed Journals

Becher, K.J. and Unger, T. (2018) 'Weakly hyperbolic involutions'. Expositiones Mathematicae, 36 :78-97. [DOI] [Details]
Astier, V. and Unger, T. (2018) 'Signatures, sums of hermitian squares and positive cones on algebras with involution'. Electronic Research Announcements in Mathematical Sciences, 25 :16-26. [DOI] [Details]
Astier, V. and Unger, T. (2017) 'Stability index for algebras with involution'. Contemporary Mathematics, 697 :41-50. [DOI] [Details]
Geerts, F; Unger, T; Karvounarakis, G; Fundulaki, I; Christophides, V (2016) 'Algebraic Structures for Capturing the Provenance of SPARQL Queries'. Journal of the ACM, 63 (1):7:1-7:63. [DOI] [Details]
Astier, V. and Unger, T. (2015) 'Signatures of hermitian forms and prime ideals of Witt groups'. Advances in Mathematics, 285 :497-514. [DOI] [Details]
Astier, V. and Unger, T. (2014) 'Signatures of hermitian forms and the Knebusch Trace Formula'. Mathematische Annalen, 358 (3-4):925-947. [DOI] [Details]
Astier, V. and Unger, T. (2013) 'Signatures of hermitian forms and applications'. Oberwolfach Reports, 10 (2):1853-1856. [DOI] [Details]
Pumplün, S. and Unger, T.; (2011) 'Space-time block codes from nonassociative division algebras'. Advances in Mathematics of Communications, 5 (3):449-471. [DOI] [Details]
Unger, T. and Markin, N.; (2011) 'Quadratic forms and space-time block codes from generalized quaternion and biquaternion algebras'. IEEE Transactions on Information Theory, 57 (9):6148-6156. [DOI] [Details]
Klep, I. and Unger, T.; (2010) 'The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution'. Journal of Algebra, 324 (2):256-268. [DOI] [Details]
Klep, I and Unger, T; (2009) 'The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution'. Oberwolfach Reports, 6 (2):1388-1390. [DOI] [Details]
Lewis, D.W. and Unger, T.; (2008) 'Hermitian Morita theory: a matrix approach'. Irish Mathematical Society Bulletin, 62 :37-41. [Details]
Astier, V. and Unger, T.; (2008) 'A hermitian analogue of the Bröcker-Prestel theorem'. Indagationes Mathematicae-New Series, 19 (3):349-358. [DOI] [Details]
Lewis, DW; Unger, T; Van Geel, J; ; (2005) 'The Hasse principle for similarity of hermitian forms'. Journal of Algebra, 285 (1):196-212. [DOI] [Details]
Lewis, DW; Unger, T; ; (2003) 'A local-global principle for algebras with involution and hermitian forms'. Mathematische Zeitschrift, 244 (3):469-477. [DOI] [Details]
Pumplun, S; Unger, T; ; (2002) 'The hermitian level of composition algebras'. Manuscripta Mathematica, 109 (4):511-525. [DOI] [Details]
Lewis, David W.; Scheiderer, Claus; Unger, Thomas; (2001) 'A weak Hasse principle for central simple algebras with an involution'. Documenta Mathematica, Extra Vol (2001):241-251. [Details]
Unger, T.; (2001) 'Clifford algebra periodicity for central simple algebras with an involution'. Communications in Algebra, 29 (3):1141-1152. [DOI] [Details]
Unger, Thomas; (2001) 'A note on surrogate forms of central simple algebras'. Proceedings of the Royal Irish Academy, 101a (2):125-135. [Details]
Unger, T.; (1998) 'Genetic Algorithms: a survey of some mathematical models'. Irish Mathematical Society Bulletin, 41 :57-71. [Details]
                                                                                                                                           

Research

Research Interests

Quadratic and hermitian forms, algebras with involution, their applications in real algebra and space-time coding.

Research Projects

Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET)
Title : Isotropy of quadratic forms and algebras with involution
Start Date / End Date : 01-AUG-09 / 31-JUL-12
Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET)
Title : Isotropy of quadratic forms and algebras with involution
Start Date / End Date : 01-AUG-09 / 31-JUL-12
Sponsor : Science Foundation Ireland (SFI)
Title : The hasse principle for weak isotropy of central simple algebras with an involution of the second kind
Start Date / End Date : 01-MAY-07 / 30-APR-10
Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET)
Title : Hermitian levels of octonion algebras (James O'Shea)
Start Date / End Date : 01-OCT-02 / 30-SEP-03