Here are pictures related to my research interests: contact geometry, singularity theory and the 3-body problem There are also videos. Depending on your computer setup, you may not be able to play them directly. The best way to still watch them, is to download the files (right click), and to then play them with the VLC-player
The standard contact structure
Links of singularities
An interesting class of contact manifolds are formed by links of singularities. Here is a picture of a smoothed singularity (one coordinate is projected out. This is the A2-singularity in C2
Orbits and knots in the restricted 3-body problem (after Levi-Civita regularization)
Hopf fibration
Here are some fibers of the famous Hopf fibration after stereographic projection.
Maslov cycle in Sp(2)
Here is a picture of the Maslov cycle. Since Sp(2) is diffeomorphic to the interior of a solid torus, and to make the picture simpler, I unrolled the solid torus after cutting out a disk. The resulting Maslov cycle was discretized with the marching cube process.
Subsets of pages of an open book
The link of a cusp singularity is the threfoil knot, and the complement fibers over the circle, giving an open book. Here are a couple of pages of the open book intersected with a cube.
Maslov cycle in Sp(2)
Here is a video of a spinning Maslov cycle (video in mp4 format)A single ball in a 3-torus
Flying around in a 3-torus (video in mp4 format)A single ball in the Poincare homology sphere
Flying around in a Poincare homology sphere (video in mp4 format)A single ball in the the circle times 2-sphere
Flying around in a product of a circle and a 2-sphere (video in mp4 format)A single ball in the Seifert-Weber hyperbolic 3-manifold
Flying around in the Seifert-Weber 3-manifold (video in mp4 format) More three manifolds coming.Billiards
A billiard (video in mpeg4 format) Same billiard (video in mpeg4 format) A 3d billiard (video in mpeg4 format)