General information

I am broadly interested in studying the relationship between the geometry and topology of a manifold, and how these constrain each other. This lies on the intersection of geometric topology, differential geometry, theory of Lie groups and algebraic groups, dynamics and ergodic theory, and metric geometry.

My research statement (for a general audience).
An extended research statement (for experts).
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Papers

My papers are available on the arXiv.

9. Coarse geometry of expanders from rigidity of warped cones (2017, 44 pages)
Joint with David Fisher and Thang Nguyen

8. Classification of normally and finitely non-co-Hopfian groups (2017, 23 pages)

7. The fundamental theorem of affine geometry on tori
Joint with Jacob Shulkin
New York J. Math. , (2017) vol. 23, 631-654.

6. Towers of regular self-covers and linear endomorphisms of tori (2016, 33 pages)
Geom. Topol., to appear

5. Rigidity of convex divisible domains in flag manifolds (2015, 52 pages)
Joint with Andrew Zimmer

4. Quasicircle boundaries and exotic almost-isometries (2014, 18 pages)
Joint with Jean-Fran├žois Lafont and Benjamin Schmidt
Ann. Inst. Fourier Vol. 67 no. 2 (2017), p. 863-877
Warning: The published version is substantially different because it does not include Section 3.

3. Isometry types of frame bundles
Pacific J. Math. (2016), vol. 285, no. 2, 393-426.

2. Symmetry gaps in Riemannian geometry and minimal orbifolds
J. Diff. Geom. (2017), vol. 105, no. 3, 487-517.

1. Riemannian manifolds with local symmetry
J. Topol. Anal. (2014), vol. 6, no. 2, 211-236,
doi: 10.1142/S179352531450006X