Associate Professor Volker Gebhardt

Associate Professor Volker Gebhardt

DAP - Mathematics and Statistics,
Mathematics & Statistics

Associate Professor,
Mathematics & Statistics

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 Associate Professor Gebhardt.

Qualifications

  • PhD University of Essen

Interests

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

Organisational Unit (School / Division)

  • Mathematics & Statistics
  • Mathematics & Statistics

Committees

  • SCEM Work Plan Committee

Contact

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

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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. (2020), 'Constructing unlabelled lattices', Journal of Algebra, vol 545 , pp 213 - 236.
  • Cumplido, M., Gebhardt, V., Gonzalez-Meneses, J. and Wiest, B. (2019), 'On parabolic subgroups of Artin-Tits groups of spherical type', Advances in Mathematics, vol 352 , pp 572 - 610.
  • Clark, C., Egri-Nagy, A., Francis, A. and Gebhardt, V. (2019), 'Bacterial phylogeny in the Cayley graph', Discrete Mathematics, Algorithms and Applications, vol 11, no 5 .
  • Gebhardt, V. and Tawn, S. (2016), 'On the penetration distance in Garside monoids', Journal of Algebra, vol 451 , pp 544 - 576.
  • Gebhardt, V. and Tawn, S. (2016), 'Zappa-Szep products of Garside monoids', Mathematische Zeitschrift, vol 282, no 1 , pp 341 - 369.
  • Dehornoy, P. and Gebhardt, V. (2014), 'Algorithms for Garside calculus', Journal of Symbolic Computation, .
  • Egri-Nagy, A., Gebhardt, V., Tanaka, M. and Francis, A. (2014), 'Group-theoretic models of the inversion process in bacterial genomes', Journal of Mathematical Biology, vol 69, no 1 , pp 243 - 265.
  • 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.
  • 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.

Previous Projects

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

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