Doctor Volker Gebhardt

• Biography
• Areas of Research / Teaching Expertise
• Grants / Current Projects
• Selected Publications
• Contact Details

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 in the School of Computing and 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.

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Areas of Research / Teaching Expertise

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

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Grants / Current Projects

Algorithmic Approaches to Braids and their Generalisations.
ARC Discovery Grant DP1094072, 2010-2012.
Volker Gebhardt (CI); Patrick Dehornoy, Juan González-Meneses.

D-modules, Singularities and Arithmetic Algebraic Geometry.
Spanish national competitive grant, Plan Nacional MTM2007-66929, 2007-2010.

Luis Narváez-Macarro (CI); Volker Gebhardt, Juan González-Meneses and 12 others.

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Selected Publications

Publications since 2005:

Volker Gebhardt and Juan González-Meneses,
Solving the conjugacy problem in Garside groups by cyclic sliding,
Journal of Symbolic Computation, in press.

Volker Gebhardt and Juan González-Meneses,
The cyclic sliding operation in Garside groups,
Mathematische Zeitschrift, in press.

Volker Gebhardt and Juan González-Meneses,
On the Cycling Operation in Braid Groups,
Discrete Applied Mathematics 156 (2008), 3072-3090.

Joan S Birman, Volker Gebhardt and Juan González-Meneses,
Conjugacy in Garside groups II: Structure of the Ultra Summit Set,
Groups, Geometry, and Dynamics 2 (2008), 13-61.

Joan S Birman, Volker Gebhardt and Juan González-Meneses,
Conjugacy in Garside groups III: Periodic Braids,
Journal of Algebra 316 (2007), 746-776.

Joan S Birman, Volker Gebhardt and Juan González-Meneses,
Conjugacy in Garside groups I: Cyclings, Powers and Rigidity,
Groups, Geometry, and Dynamics 1 (2007), 221-279.

Volker Gebhardt,
Conjugacy search in braid groups: from a braid-based cryptography point of view,
Applicable Algebra in Engineering, Communication and Computing 17 (2006), 219-238.

Volker Gebhardt,
Computer Aided Discovery of a Fast Algorithm for Testing Conjugacy in Braid Groups.
in Bosma, Cannon (Eds.): Discovering Mathematics with Magma,
Algorithms and Computation in Mathematics 19, Springer, 2006.

Volker Gebhardt,
A new approach to the conjugacy problem in Garside groups,
Journal of Algebra 292 (2005), 282-302.

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