Friedrich Bauermeister

I am interested in differential geometry, topology, and more generally in mathematics related to and inspired by physics.

If you ever want to collaborate, do not hesitate to reach out to me at friedrich.bauermeister.gr(at)dartmouth.edu !

At this moment there are two areas of research I am pursuing.

Causality and geodesic refocusing

I am researching the interplay of causal structures of globally hyperbolic spacetimes with their topologies. In particular, I am interested in what the presence of refocusing of null-geodesics tells us about the spacetimes topology. These questions have natural analogues in Riemannian geometry: Given the presence of (families of) closed geodesics in a Riemannian manifold, what can we say about its topology? It turns out that some statements of this type in the Riemannian setting can be lifted to the Lorentzian setting, where they can be solved using Lorentzian techniques. Some statements in the Lorentzian setting can further be lifted to statements in contact geometry, which allows the use of contact geometric techniques to prove Lorentzian results.

Thick knot theory and disentanglement problems

An embedding of a knot in 3-dimensional Euclidean space which has its unit-radius normal disk bundle embedded is called a thickly embedded knot. Questions of thick knot theory are: Given a topological knot, what is the length of the shortest realization of it as a thickly embedded knot? Are there local minima of the length functional in the space of thickly embedded knots or links? Are there in the space of topologically trivial thickly embedded knots or lengths? If so, this would correspond to a physical configuration of rope which is topologically trivial but which cannot be physically untangled. These questions, while easy to state, are surprisingly hard to answer.

Preprints:

Topological consequences of null-geodesic refocusing and applications to Z^x manifolds (slides of talk about this paper)

Gordian split links in the Gehring ropelength problem (slides of talk about this paper)

Strata of toric hyperplane arrangements, zonotope lattice points, and the Bondal-Thomsen collection (Results of an REU I participated in as a teaching assistant.)

Seminar and conference talks:

Gordian split links in the Gehring ropelength problem

Invited talk, Five-College Geometry & Topology Seminar (University of Massachusetts Amherst), Sep 2025.

Topological consequences of null-geodesic refocusing and applications to Z^x manifolds

Contributed talk, Topology Seminar (Dartmouth College), May 2025.

Topological consequences of null-geodesic refocusing and applications to $Z^x$ manifolds

Contributed talk, Knots in Washington (George Washington University), Apr 2025.

Local ropelength minima and Gordian unlinks

Contributed talk, Knots in Washington (George Washington University), Apr 2024.

“History proves that physics has not only forced us to choose among problems which came in a crowd; it has imposed upon us such as we should without it never have dreamed of. However varied may be the imagination of man, nature is still a thousand times richer. To follow her we must take ways we have neglected, and these paths lead us often to summits whence we discover new countries. What could be more useful! ” – Henri Poincaré