Research

I obtained my PhD in 2012 at Utrecht University under supervision of Hans Duistermaat, Erik van den Ban, and Heinz Hanßmann. I worked on persistence of noncompact normally hyperbolic invariant manifolds; I have extended this theory to a setting of general Riemannian manifolds under the assumption of bounded geometry. My PhD thesis is available below, see my CRmath article for a brief statement of the results.

My recent work includes applications of normal hyperbolicity to network dynamics and biomechanics. At Imperial College I furthermore worked on geometric mechanics approaches to image registration and fluid dynamics. In a current project with Heinz Hanßmann, we look at persistence of normally hyperbolic KAM tori, where we pay special attention to the boundary of the invariant manifold.

Another long-standing research project originating from my PhD work is to investigate nonholonomically constrained systems as reduced systems and the question of which friction forces realize the Lagrange-d'Alembert description of such systems in the limit of infinite friction. See my talk given at the AIMS 2016 conference and my recent paper on realizing nonholonomic dynamics. I also work on this in a Poisson geometry setting with Paula Balseiro and Larry Bates.

Cover of Normally Hyperbolic Invariant Manifolds — The Noncompact Case

Publications

Research monograph:

Articles:

See also my ORCID and ResearcherID, and my articles on arXiv and MathSciNet.

A list of errata to my published works is available. Additional corrections are gratefully welcomed!

PhD thesis: Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry, 229 pages, August 2012.
Written under supervision of Prof.dr. Hans Duistermaat, Dr. Heinz Hanßmann, and Prof.dr. Erik van den Ban at Utrecht University. (UU archive, PDF, arXiv)

MSc thesis: The polygon model for 2+1D gravity: the constraint algebra and problems of quantization, 67 pages.
Written under supervision of Prof.dr. Renate Loll at Utrecht University. (PDF, arXiv)

Presentations

I have given or will give the following talks/presentations: