Doctor Volker Gebhardt

Doctor Volker Gebhardt

Associate Professor,
Mathematics

Biography

Dr Volker Gebhardt completed his PhD at the University of Essen, Germany in the field of computational group theory. He spent the next four years as a post-doctoral researcher with the Computational Algebra group at the University of Sydney. In 2003-2004, he joined the University of Western Sydney as a casual lecturer and taught several Computing units. In July 2004, he took up a permanent position as a lecturer in Mathematics. His broad research interests lie in various areas of algebra and discrete mathematics; and he is especially interested in questions with an algorithmic or computational flavour.

This information has been contributed by Doctor Gebhardt.

Qualifications

  • PhD University of Essen

Interests

  • Combinatorial Group Theory
  • Combinatorics
  • Garside Groups
  • Group Based Cryptography

Organisational Unit (School / Division)

  • Mathematics

Committees

  • SCEM Work Plan Committee

Contact

Email: V.Gebhardt@westernsydney.edu.au
Phone: (02) 47360 688
Mobile:
Location: Y.3.55
Penrith (Kingswood)
Website:

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Teaching

Previous Teaching Areas

  • 200242 Mathematics for Engineers 3, 2012
  • 300699 Discrete Structures and Complexity, 2012

Publications

Chapters in Books

  • Gebhardt, V. (2006), 'Computer Aided Discovery of a Fast Algorithm for Testing Conjugacy in Braid Groups', Discovering Mathematics with Magma, Springer Verlag 3540376321.

Journal Articles

  • Gebhardt, V. and Tawn, S. (2016), 'On the penetration distance in Garside monoids', Journal of Algebra, vol 451 , pp 544 - 576.
  • Berrick, J., Gebhardt, V. and Paris, L. (2014), 'Finite index subgroups of mapping class groups', Proceedings of the London Mathematical Society, vol 108, no 3 , pp 575 - 599.
  • Gebhardt, V. and Tawn, S. (2014), 'Normal forms of random braids', Journal of Algebra, vol 408 , pp 115 - 137.
  • Gebhardt, V. and Gonzalez-Meneses, J. (2013), 'Generating random braids', Journal of Combinatorial Theory, Series A, vol 120, no 1 , pp 111 - 128.
  • Gebhardt, V. (2013), 'Computing growth functions of braid monoids and counting vertex-labelled bipartite graphs', Journal of Combinatorial Theory. Series A, vol 120, no 1 , pp 232 - 244.
  • Dehornoy, P. and Gebhardt, V. (2013), 'Algorithms for Garside calculus', Journal of Symbolic Computation, .
  • Egri-Nagy, A., Gebhardt, V., Tanaka, M. and Francis, A. (2013), 'Group-theoretic models of the inversion process in bacterial genomes', Journal of Mathematical Biology, .
  • Gebhardt, V. and Gonzalez-Meneses, J. (2010), 'The cyclic sliding operation in Garside groups', Mathematische Zeitschrift, vol 265, no 1 , pp 85 - 114.
  • Gebhardt, V. and Gonzalez-Meneses, J. (2010), 'Solving the conjugacy problem in Garside groups by cyclic sliding', Journal of Symbolic Computation, vol 45, no 6 , pp 629 - 656.
  • Birman, J., Gebhardt, V. and Gonzalez-Meneses, J. (2008), 'Conjugacy in Garside groups II : structure of the ultra summit set', Groups, Geometry, and Dynamics, vol 2 , pp 13 - 61.
  • Gonzalez-Meneses, J. and Gebhardt, V. (2008), 'On the cycling operation in braid groups', Discrete Applied Mathematics, vol 156, no 16 , pp 3072 - 3090.
  • Birman, J., Gebhardt, V. and Gonzalez-Meneses, J. (2007), 'Conjugacy in Garside groups I: cyclings, powers and rigidity', Groups, Geometry, and Dynamics, vol 1 , pp 221 - 279.
  • Birman, J., Gebhardt, V. and Gonzalez-Meneses, J. (2007), 'Conjugacy in Garside groups III: Periodic Braids', Journal of Algebra, vol 316, no 2 , pp 746 - 776.
  • Gebhardt, V. (2006), 'Conjugacy search in braid groups: from a braid-based cryptography point of view', Applicable Algebra in Engineering, Communication and Computing, vol 17, no 40636 , pp 219 - 238.
  • Gebhardt, V. (2005), 'A new approach to the conjugacy problem in Garside groups', Journal of Algebra, vol 292, no 1 SPEC. ISS. , pp 282 - 302.

Conference Papers

  • Egri-Nagy, A., Francis, A. and Gebhardt, V. (2014), 'Bacterial genomics and computational group theory : the BioGAP package for GAP', International Congress of Mathematical Software, Seoul, South Korea.

Research

Previous Projects

Title: Algebraic algorithms for investigating the space of bacterial genomes
Years: 2013-01-01 - 2015-12-31
ID: P00020822
Western Researchers: Andrew Francis and Volker Gebhardt
Funding:
  • Australian Research Council (ACRG)
Title: Charting unkown territory: an enumerative approach to Garside groups
Years: 2013-12-10 - 2015-06-30
ID: P00021939
Western Researchers: Volker Gebhardt
Funding:
  • University of Western Sydney
Title: Algorithmic Approaches to Braids and their Generalisations
Years: 2010-09-30 - 2013-12-30
ID: P00016834
Western Researchers: Volker Gebhardt
Funding:
  • Australian Research Council (ACRG)

University of Western Sydney

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