Associate Professor Volker Gebhardt
Dap  Mathematics and Statistics,
Mathematics
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 postdoctoral researcher with the Computational Algebra group at the University of Sydney. In 20032004, 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
 Mathematics
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., GonzalezMeneses, J. and Wiest, B. (2019), 'On parabolic subgroups of ArtinTits groups of spherical type', Advances in Mathematics, vol 352 , pp 572  610.
 Clark, C., EgriNagy, 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), 'ZappaSzep 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, .
 EgriNagy, A., Gebhardt, V., Tanaka, M. and Francis, A. (2014), 'Grouptheoretic 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 GonzalezMeneses, 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 vertexlabelled bipartite graphs', Journal of Combinatorial Theory, Series A, vol 120, no 1 , pp 232  244.
 Gebhardt, V. and GonzalezMeneses, J. (2010), 'The cyclic sliding operation in Garside groups', Mathematische Zeitschrift, vol 265, no 1 , pp 85  114.
 Gebhardt, V. and GonzalezMeneses, 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 GonzalezMeneses, J. (2008), 'Conjugacy in Garside groups II : structure of the ultra summit set', Groups, Geometry, and Dynamics, vol 2 , pp 13  61.
 GonzalezMeneses, 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 GonzalezMeneses, 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 GonzalezMeneses, 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 braidbased 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
 EgriNagy, 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: 

Western Researchers:  Andrew Francis and Volker Gebhardt 
Years:  20130101  20151231 
ID:  P00020822 
Title:  Charting unkown territory: an enumerative approach to Garside groups 
Funder: 

Western Researchers:  Volker Gebhardt 
Years:  20131210  20150630 
ID:  P00021939 
Title:  Algorithmic Approaches to Braids and their Generalisations 
Funder: 

Western Researchers:  Volker Gebhardt 
Years:  20100930  20131230 
ID:  P00016834 