Matthew Romney

I am a Simons Instructor at Stony Brook University, from September 2020 to August 2023. I received my PhD in 2017 from the University of Illinois under the supervision of Jeremy Tyson. Prior to this, I obtained bachelor's and master's degrees at the Brigham Young University with Michael Dorff.

Before arriving at Stony Brook, I was a postdoctoral researcher at the University of Jyväskylä in Finland (2018-2019) and at the University of Cologne in Germany (Spring 2020).

CV

My research interests are in metric geometry and analysis on metric spaces, with an emphasis on quasiconformal geometry and uniformization of surfaces. For a broad, nontechnical survey of the field, I'd recommend the survey Nonsmooth calculus by Juha Heinonen.

Contact:
matthew.romney (at) stonybrook (dot) edu

Office: Math Tower 4101B Mathematics Department
Stony Brook University
  Stony Brook, NY, 11794-3651

Publications

  1. Triangulating metric surfaces (preprint)
    with P. Creutz.
  2. The branch set of minimal disks in metric spaces (preprint)
    with P. Creutz.
  3. Quasiconformal geometry and removable sets for conformal mappings (preprint)
    J. Anal. Math., to appear, with T. Ikonen.
  4. Uniformization with infinitesimally metric measures (preprint)
    J. Geom. Anal., to appear, with K. Rajala and M. Rasimus.
  5. On the inverse absolute continuity of quasiconformal mappings on hypersurfaces (preprint)
    Amer. J. Math., to appear, with D. Ntalampekos.
  6. Singular quasisymmetric mappings in dimensions two and greater
    Adv. Math., 351: 479-494, 2019.
  7. Reciprocal lower bound on modulus of curve families in metric surfaces
    Ann. Acad. Sci. Fenn. Math., 44(2): 681-692, 2019, with K. Rajala.
  8. Quasiconformal parametrization of metric surfaces with small dilatation
    Indiana Univ. Math. J., 68(3): 1003-1011, 2019. (Some remarks)
  9. Sums of asymptotically midpoint uniformly convex spaces
    Bull. Belg. Math. Soc. Simon Stevin, 24(3): 439-446, 2017, with S. Dilworth, D. Kutzarova and N.L. Randrianarivony.
  10. Quasiconformal mappings on the Grushin plane
    Math. Z., 297(3-4): 915-928, 2017, with C. Gartland and D. Jung.
  11. Bi-Lipschitz embedding of the generalized Grushin plane in Euclidean spaces
    Math. Res. Lett., 24(4): 1179-1205, 2017, with V. Vellis.
  12. Conformal Grushin spaces
    Conform. Geom. Dyn., 20: 97-115, 2016.
  13. Univalency of convolutions of harmonic mappings
    Appl. Math. Comput. 234: 326-332, 2014, with Z. Boyd, M. Dorff, M. Nowak, M. Wołoszkiewicz.