Chair in Pure Mathematics
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+44 (0)1224 272603
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+44 (0)1224 272607
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m.geck@abdn.ac.uk
http://www.abdn.ac.uk/~mth190
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Meston Building, room 319
Chair in Pure Mathematics, Head of Department
Dipl-Math PhD Habilitation (RWTH Aachen)
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Personal Details
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Research Interests
My main area of research is the representation theory of finite groups of Lie type (or finite reductive groups) and the study of related structures, like Hecke algebras and Coxeter groups. I am also one of the developers of the computer algebra system CHEVIE, which allows symbolic calculations with the above objects.
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Brief CV
1988-1995 Research assistant, Lehrstuhl D für Mathematik, RWTH Aachen (Germany)
1990 PhD, RWTH Aachen
1994 Habilitation, RWTH Aachen
1995-1999 CNRS (permanent) research position, Équipe des Groupes Finis, Université Paris 7 (France).
1999-2005 Professor of Mathematics, Université Lyon 1 (France)
Since 2005 6th Century Chair in Mathematics, University of Aberdeen
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Some External Responsibilities
2001-2004 Scientific Director of the Mathematical Library, Université Lyon 1
2004-2010 Editor of the Journal of Algebra, section "Computational Algebra"
Since 2004 Editor of the Carpathian Journal of Mathematics
2005 Co-organiser, together with D. Testerman and J. Thévenaz, of a research semester (6 months) "Group Representation Theory", Bernoulli Center, EPFL Lausanne (Switzerland)
2008-2010 Member of the Academic Steering Committee of the SMSTC (Scottish Mathematical Sciences Training Centre)
2008, 2011 Member of an EPSRC peer review panel.
2009 Co-organiser, together with S. Kleshchev and G. Roehrle, of a research semester (6 months) "Algebraic Lie Theory", Isaac Newton Institute, Cambridge (UK)
2009-2010 Head of Teaching for Mathematics in the School of Natural and Computing Sciences
2009- Adviser of Studies
2010 Member of the Review Panel for the DFG Priority Programme "Algorithmische und experimentelle Methoden in Algebra, Geometrie und Zahlentheorie"
2010 Member of the jury junior IUF (Institut Universitaire de France), by nomination of the French Minister of Education
2010-2012 Head of Department for Mathematics in the School of Natural and Computing Sciences
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Awards
1991 Together with K. Lux: "Bennigsen-Foerder Preis" of the federal state Nordrhein-Westfalen (Germany)
1993-1996 DFG Research Grant (Ge 764/1-2), together with Klaus Lux, in the framework of the Priority Programme "Algorithmische Algebra und Zahlentheorie"
2008-2010 Principal Investigator EPSRC Network Grant EP/F029381/1, "Representation Theory Across the Channel"
2009-2012 Principal Investigator EPSRC Grant EP/G055335/1, "HPC-GAP:
High Performance Computational Algebra and Discrete Mathematics" (joint
proposal with St Andrews and Edinburgh)
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Selected Publications
Geck, M. and Mueller, J., James' conjecture for Hecke algebras of exceptional type I. Special issue in honour of Gus Lehrer, J. Algebra 321 (2009), 3274-3298.
Geck, M., Hecke algebras of finite type are cellular. Invent. Math. 169 (2007), 501-517.
Geck, M., Modular principal series representations. Int. Math. Res. Notices, vol. 2006, Article ID 41957, pp. 1-20.
Geck, M., Kazhdan--Lusztig cells and the Murphy basis, Proc. London Math. Soc. 93 (2006), 635--665.
Geck, M., An introduction to algebraic geometry and algebraic groups. Oxford Graduate Texts in Mathematics. vol. 10, Oxford University Press, New York 2003. ix+307pp., ISBN: 0-19-852831-0.
Geck, M., Character values, Schur indices and character sheaves, Represent. Theory 7 (2003), 19--55 (electronic).
Geck, M. and Pfeiffer, G., Characters of finite Coxeter groups and Iwahori--Hecke algebras. London Math. Soc. Monographs, New Series vol. 21, Oxford University Press, New York 2000. xvi+446 pp., ISBN: 0-19-850250-8.
Geck, M., Iancu, L. and Malle, Weights of Markov traces and generic degrees. Indag. Mathem., N.S., 11 (2000), 379--397.
Geck, M. and Malle, G., On the existence of a unipotent support for the irreducible characters of finite groups of Lie type. Trans. Amer. Math. Soc. 352 (2000), 429--456.
Geck, M. and Malle, G., On special pieces in the unipotent variety. Experimental Math. 8 (1999), 281--290.
Geck, M., Representations of Hecke algebras at roots of unity. Seminaire Bourbaki, 50eme annee, 1997-98, Asterisque No. 252 (1998), Exp. 836, 33--55.
Geck, M. and Lambropoulou, S., Markov traces and knot invariants related to Hecke algebras of B-type. J. reine angew. Math. 482 (1997), 191--213.
Geck, M. and Rouquier, R., Centers and simple modules for Iwahori-Hecke algebras. In: Finite reductive groups: Related structures and representations (ed. M. Cabanes), pp. 251--272, Progress in Mathematics, vol. 141, Birkhauser, Basel, 1997.
Bleher, F., Geck, M. and Kimmerle, W., Automorphisms of integral group rings of finite Coxeter groups and Iwahori--Hecke algebras. J. Algebra 197 (1997), 615--655.
Geck, M., Hiss, G. and Malle, G., Towards a classification of the irreducible representations in non-defining characteristic of a finite group of Lie type. Math. Z. 221 (1996), 353--386.
Geck, M., The decomposition numbers of the Hecke algebra of type E_6. Math. Comp. 61 (1993), 889--899.
Geck, M. and Pfeiffer, G., On the irreducible characters of Hecke algebras. Advances in Math. 102 (1993), 79--94.
Geck, M., Brauer trees of Hecke algebras. Comm. Algebra 20 (1992), 2937--2973.
Geck, M. and Hiss, G, Basic sets of Brauer characters of finite groups of Lie type. J. reine und angew. Math. 418 (1991), 173-188.
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