Kathryn Lindsey

Shapes of polynomial Julia sets

Any Jordan curve in the complex plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Finite collections of disjoint Jordan domains can be approximated by the basins of attraction of rational maps.

Horocycle flow orbits and lattice surface characterizations

The orbit closure of any translation surface under the horocycle flow in almost any direction equals its

On ergodic transformations that are both weakly mixing and uniformly rigid

SL_2(\mathbb{R})

Counting invariant components of hyperelliptic translation surfaces

orbit closure. This result gives rise to new characterizations of lattice surfaces in terms of the hororcycle flow.