(Upcoming/recent talks here)

Math papers, preprints, projects.

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  • Counting in groups: Fine asymptotic geometry,
    Notices of the AMS 63, No. 8 (2016), 871--874.
    (Published version; see also Cover and Explanation)
  • Rational growth in the Heisenberg group (with Mike Shapiro), submitted.
    (math.GR/1411.4201, most recent)
  • Random nilpotent groups I
    (with Matt Cordes, Yen Duong, Turbo Ho, and Andrew Sánchez), IMRN, to appear. (math.GR/1506.01426)
  • A sharper threshold for random groups at density one-half
    (w/ Kasia Jankiewicz, Shelby Kilmer, Samuel Lelièvre, John Mackay, and Andrew Sánchez),
    Groups, Geometry, and Dynamics Groups 10, No. 3 (2016), 985--1005.
  • Equations in nilpotent groups (with Hao Liang and Mike Shapiro),
    Proceedings of the AMS 143 (2015), 4723--4731. (math.GR/1401.2471)
  • Statistical hyperbolicity in Teichmüller space (with S Dowdall and H Masur),
    GAFA, Volume 24, Issue 3 (2014), 748--795. (math.GR/1108.5416; Most recent)
  • Spheres in the curve complex (with Spencer Dowdall and Howard Masur),
    In the Tradition of Ahlfors and Bers, Contemp. Math. 590 (2013), 1--8.
    (math.GT/1109.6338; Most recent)
  • Fine asymptotic geometry in the Heisenberg group (with Christopher Mooney),
    Indiana Univ. Math Journal 63 No. 3 (2014), 885--916. (math.GR/1106.5276, Most recent)
  • The geometry of spheres in free abelian groups
    (with Samuel Lelièvre and Christopher Mooney),
    Geom. Dedicata, Vol 161, Issue 1 (2012), 169--187. (math.GR/1004.0053; More recent)
  • Statistical hyperbolicity in groups (with Samuel Lelièvre and Christopher Mooney),
    Algebraic and Geometric Topology 12 (2012) 1--18. (math.GR/1104.4460; Most recent)
  • The sprawl conjecture for convex bodies
    (with Samuel Lelièvre and Christopher Mooney),
    Experimental Mathematics, Volume 22, Issue 2 (2013), 113--122. (PDF)
  • Pushing fillings in right-angled Artin groups
    (with Aaron Abrams, Noel Brady, Pallavi Dani, and Robert Young),
    Journal of the LMS, Vol 87, Issue 3 (2013), 663--688. (math.GR/1004.4253; Most recent)
  • Filling loops at infinity in the mapping class group
    (with Aaron Abrams, Noel Brady, Pallavi Dani, and Robert Young),
    Michigan Math J., Volume 61, Issue 4 (2012), 867--874. (math.GR/1109.6048)
  • Length spectra and degeneration of flat metrics (with Chris Leininger and Kasra Rafi), Inventiones Math., Vol 182, Issue 2 (2010), 231--277. (math.GT/0907.2082; More recent)
  • Divergence of geodesics in Teichmüller space and the mapping class group
    (with Kasra Rafi),
    GAFA, Volume 19, Issue 3 (2009), 722--742. (math.GT/0611.5359)
  • Stars at infinity in Teichmüller space in deep freeze.
  • Curvature, stretchiness, and dynamics
    In the Tradition of Ahlfors and Bers IV, Contemp. Math. 432 (2007).
  • Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry
    University of Chicago dissertation (2005). (math.GT/0508046)

Other research activity.

  • I am running a research team called the Metric Geometry and Gerrymandering Group (MGGG). We maintain a website for our planned Geometry of Redistricting Summer School, which includes information for signing up for our mailing list.
  • I'll be hosting a 10-person Research cluster on Rational Billiards at Tufts in Summer 2017. There was a similar cluster in Summer 2014 on the topic of Random Groups.
  • I ran the Undergraduate Faculty Program at PCMI 2012. This was a Research Lab in geometric group theory for 16 college professors.
  • Principal investigator for NSF grant DMS-0906086, Metric geometry of groups and surfaces, 2009-2012, DMS-1207106, Finer coarse geometry, 2012-2015, and DMS-1255442, CAREER: Finer coarse geometry, 2013-2018.
  • I was a member of a recent SQuaRE (small working group) at the American Institute of Mathematics (AIM) on Higher divergence functions together with Aaron Abrams, Noel Brady, Pallavi Dani, and Robert Young.
  • For the 2006-07 school year, I led a VIGRE-funded Research Focus Group at UC Davis on the subject of Geometric Group Theory.


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