Research InterestsMy research is in differential geometry, Teichmuller theory, and geometric structures. I am also interested in general relativity and other connections to physics.
I am starting a Junior Professorship at Heidelberg on October 1. You can find me at https://www.mathi.uni-heidelberg.de/~psmillie/.
- Unstable minimal surfaces in symmetric spaces of non-compact type (with N. Sagman). ArXiv: 2208.04885.
Completeness of hyperbolic surfaces in Minkowski 3-space. (with F. Bonsante and A. Seppi) arXiv: 2207.10019.
Unstable minimal surfaces in R^n and in products of hyperbolic surfaces. (with V. Markovic and N. Sagman). ArXiv: 2206.02938.
- Complete CMC hypersurfaces in Minkowski (n+1)-space.
(with F. Bonsante and A. Seppi). Arxiv: 1912.05477. To appear in Comm. Anal. Geom.
- Entire surfaces of constant curvature in Minkowski 3-space. (with F. Bonsante and A. Seppi). Math. Ann. 374 (2019), 1261-1309.
- On the bordification of outer space. (with K.-U. Bux, K. Vogtmann). J. London Math Soc. 98, Issue 1 (2018), 12-34.
- The number of convex triangulations of the sphere by triangles, squares, or hexagons. (with P. Engel). Geom. Topology. 22, No. 5 (2018), 2839-2864.