I am a postdoc from the Research Foundation -- Flanders (FWO-Vlaanderen). During the Fall of 2009, I was a JSPS research fellow working with Hiroaki Yoshimura at Waseda University (Japan). In 2007-2009, I was a Fulbright postdoc with Jerrold Marsden at CDS in Caltech. I completed my Ph.D. thesis at Ghent University (Belgium) at the former Department of Mathematical Physics and Astronomy.

My current research interests include the following (in order of definiteness):

• Geometric reduction for solid bodies in vortical flow;
• Variational principles in field theory and Dirac structures;
• Space/time adapting discretizations of field theories;
• Everything else :-)

Contact

Joris Vankerschaver
Department of Mathematics
Ghent University
Krijgslaan 281 -- S9
B-9000 Ghent, Belgium

E-mail: Joris.Vankerschaver <at> UGent.be

What's new

• I recently started playing with Sage, a flexible open-source mathematics environment written in Python. Among other things, I implemented some of the potential flow examples that I use in my course on Continuum Mechanics. For now, see my description of rigid bodies in potential flow with circulation. Eventually, I plan to give this its own space on the web.
• My paper "Geometric Control of Particle Manipulation in a Two-Dimensional Fluid" with Yizhar Or, S. D. Kelly, J. E. Marsden and R. M. Murray was awarded the Guan Zhao-Zhi award at the 2009 CDC-CCC.
• Caltech undergrad Raymond Jimenez just finished his FSRI project on numerical optimizations of Lagrangian Coherent Structures using nVidia's CUDA api for GPU programming. See the results here. Update: Raymond's results can also be found on the nVidia CUDA page.

Publications

Preprints:

• J. Vankerschaver, H. Yoshimura, J. E. Marsden. Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac Structures. Submitted to Proc. 49th Control and Decision Conference.
• J. Vankerschaver, E. Kanso, J. E. Marsden. The Dynamics of a Rigid Body in Potential Flow with Circulation. Accepted for publication in Reg. Chaot. Dyn. [abs] [pdf]

Published:

• B. Langerock, F. Cantrijn, J. Vankerschaver. Routhian reduction for quasi-invariant Lagrangians. J. Math. Phys. 51 (2010) 022902. [abs] [pdf] [doi]
• Cedric M. Campos, Manuel de Leon, David Martin de Diego, Joris Vankerschaver. Unambiguous Formalism for Higher-Order Lagrangian Field Theories. J. Phys. A: Math. Theor. 42 (2009) 475207. [abs] [pdf] [doi]
• J. Vankerschaver, E. Kanso, J. E. Marsden. The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices. J. Geom. Mech. 1 (2009), no. 2, 223--266. [abs] [pdf] [doi]
• Symmetry aspects for nonholonomic field theories. J. Phys. A: Math. Theor. 41 (2008), 035401. (with D. Martin de Diego). [abs] [pdf] [doi]
• Euler-Poincaré reduction for discrete field theories. J. Math. Phys. 48 (2007), 032902. [abs] [pdf] [doi]
• Nonholonomic kinematic constraints in elasticity. J. Phys. A: Math. Theor. 40 (2007), no. 14, 3389--3913. [abs] [pdf] [doi]
• Discrete Lagrangian field theories on Lie groupoids. J. Geom. Phys. 57 (2007), no. 2, pp. 665--689. (with F. Cantrijn). [abs] [pdf] [doi]
• The Momentum Map for Nonholonomic Field Theories with Symmetry. Int. J. Geom. Meth. Mod. Phys. 2 (2005), no. 6, pp. 1029--1041. [abs] [pdf] [doi]
• Geometric aspects of nonholonomic field theories. Rep. Math. Phys. 56 (2005), no. 3, pp. 387--411 (with F.Cantrijn, M. de Leon, and D. Martin de Diego). [abs] [pdf] [doi]

Conference Proceedings:

• Yizhar Or, Joris Vankerschaver, Scott D. Kelly, Richard M. Murray and Jerrold E. Marsden. Geometric Control of Particle Manipulation in a Two-Dimensional Fluid. Proc. 48th Control and Decision Conf, Shanghai. Preprint. This paper was awarded the Guan Zhao-Zhi Award at the 2009 CDC-CCC.
• J. Vankerschaver, E. Kanso, J.E. Marsden. The motion of solid bodies in potential flow with circulation: a geometric outlook. Proceedings of DSCC ASME 2008 Dynamic Systems and Control Conference. [pdf]
• J. Vankerschaver. A connection-theoretic approach to the analysis of symmetries of nonholonomic field theories. Proc. 10th Conf. on Differential Geometry and its Applications, World Sci. Publ., River Edge, NJ, 2008, 703-711. [pdf]
• F. Cantrijn, J. Vankerschaver. The Skinner-Rusk approach for vakonomic and nonholonomic field theories. In: F. Cantrijn et al (eds.), Differential geometric methods in mechanics and field theory, Volume in honour of Willy Sarlet (2007), 1-14. [pdf]
• J. Vankerschaver. Classical field theories with external constraints. Proc. XIV Fall Workshop on Geometry and Physics. Publicaciones de la RSME, vol. 10 (2006), 285-291. [pdf]

PhD Thesis:

• Continuous and discrete aspects of classical field theories with nonholonomic constraints. PhD diss., Ghent University, 2007. PDF

Teaching

• CDS-140b (2009): Introduction to Dynamical Systems.

Conferences and Talks

Upcoming (2010)

• 04/25-04/28: Institut Elie Cartan, Universite de Nancy (Nancy, France)
• 05/25-05/28: 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications (TU Dresden, Germany)

Previous (2009)

• 12/14-12/16: 48th IEEE Conference on Decision and Control (Shanghai, China)
• 11/30: Mathematics seminar, Keio University, Japan.
• 11/23 and 12/06: Mathematics seminar, Waseda University, Japan.
• 08/24-08/30: XXIV International Workshop on Differential Geometric Methods in Theoretical Mechanics (Levico Terme, Italy)
• 05/17-05/21: SIAM Conference on Applications of Dynamical Systems (Snowbird, Utah)
• 05/14: Groupoid Seminar, UC Riverside.
• 05/07-05/08: 5th Structured Integrators meeting (Caltech)
• 04/18: 3rd Southern California Symposium on Flow Physics (UC San Diego, CA) My extended abstract.
• 04/13: CDS Group Seminar (Caltech)

2008

• 12/16-12/18: International Young Researchers Workshop on Geometry, Mechanics and Control (Barcelona, Spain)
• 12/12: Talk, Department of Mathematics and Statistics (University of Surrey, UK)
• 11/23-11/25: 2008 APS Division of Fluid Dynamics meeting (San Antonio, Texas)
• 11/22: Groupoidfest (UC Riverside, CA). Slides.
• 10/20-10/22: 2008 ASME Dynamic Systems and Control Conference (Ann Arbor, Michigan).
• 07/20-07/26: Applied Dynamics and Geometric Mechanics (Oberwolfach, Germany).
• 05/30: Maseeh Mathematics & Statistics Colloquium Series (Portland State University, Oregon).
• 05/18-05/21: 7th AIMS conference on dynamical systems (University of Texas at Arlington).
• 04/24: 4th Annual Structured Integrators Workshop (Stanford).
• 03/12: Lunchtime Seminar (University of Southern California).