Anna Parlak

I am leading the Low-Dimensional Topology group at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany.

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My main objects of interest are pseudo-Anosov flows on closed orientable three-manifolds, as well as flows obtained from them by drilling out finitely many closed orbits.

I study these flows mostly using combinatorial structures called veering triangulations. Every pseudo-Anosov flow can be encoded by infinitely many veering triangulations, and conversely, every veering triangulation encodes infinitely many pseudo-Anosov flows. The connection between veering triangulations and pseudo-Anosov flows passes through certain bi-foliated planes called loom spaces.

My research interests include the combinatorics of veering triangulations, the properties of their associated loom spaces, the relationships between different veering triangulations encoding the same flow, and the interplay between the combinatorics of veering triangulations and the dynamics of pseudo-Anosov flows.

 

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