I’m in the process of updating this page with math and interdisicplinary papers!

Math Papers, Preprints, Projects

• 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. (math.GR/1412.8741)
• 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 hosted 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.