Steven Frankel

Steven Frankel 208 Cupples I Department of Mathematics Washington University in St Louis steven.frankel@wustl.edu

Research

I am interested in geometric topology and dynamics, especially in combination: 3-manifolds, foliations, and hyperbolic geometry, quasigeodesic and pseudo-Anosov flows, partially hyperbolic diffeomorphisms, groups acting on circles, trees, and spheres, etc.

You can watch short talks about quasigeodesic flows here and here.

Publications

• Quasigeodesic flows and Mobius-like groups,
  J. Diff. Geom. 93 (2013), no. 3, 401-429
  [PDF, arXiv]


• Quasigeodesic flows from infinity,
  PhD thesis, University of Cambridge (2013)
  [PDF]


• Quasigeodesic flows and sphere-filling curves,
  Geom. Topol. 19 (2015), no. 3, 1249-1262
  [PDF, arXiv]


• Coarse hyperbolicity and closed orbits for quasigeodesic flows,
  Ann. of Math. (2) 188 (2018), no. 1, 1-48
  [PDF, arXiv]


• Research announcement: Partially hyperbolic diffeomorphisms homotopic to the identity on 3-manifolds (with T. Barthelme, S. Fenley, and R. Potrie),
  2018 MATRIX Annals. Eds. D.R. Wood, J. de Gier, C.E. Praeger, T. Tao. Springer International Publishing, 2020.
  [PDF, arXiv]


• Dynamical incoherence for a large class of partially hyperbolic diffeomorphisms (with T. Barthelme, S. Fenley, and R. Potrie),
  Ergod. Theory Dyn. Syst. 41 (2021), no. 11, 3227-3243
  [PDF, arXiv]


• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case (with T. Barthelme, S. Fenley, and R. Potrie),
  Ann. Sci. Éc. Norm. Supér. 57 (2024), no. 2, 293-349
  [arXiv]


• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part II: Branching foliations (with T. Barthelme, S. Fenley, and R. Potrie),
  Geom. Topol. 27 (2023), no. 8, 3095-3181
  [arXiv]


• Orbit equivalences of pseudo-Anosov flows (with T. Barthelme and K. Mann),
  Invent. Math. (2025)
  [arXiv]


• From veering triangulations to link spaces and back again (with S. Schleimer and H. Segerman),
  to appear in Mem. Amer. Math. Soc.
  [arXiv]


• From quasigeodesic to pseudo-Anosov flows (with M. Landry),
  preprint available upon request