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 work is supported by NSF DMS-1855371 and DMS-2203867.


My publications are available on the arXiv.

14. Greenberg-Shalom's commensurator arithmeticity hypothesis and applications
With N. Brody, D. Fisher and M. Mj

13. Co-spectral radius of intersections
With M. Frączyk
Ergodic Theory and Dynamical Systems (2023), p. 1-15. doi:10.1017/etds.2023.21

12. Commensurators of normal subgroups of lattices
With D. Fisher and M. Mj

11. Cantor dynamics of renormalizable groups
With S. Hurder and O. Lukina
Groups, Geom. Dyn., vol. 15 (2021), no. 4, 1449-1487.

10. Heat kernels are not uniform expanders
With M. Frączyk

9. Rigidity of warped cones and coarse geometry of expanders
With D. Fisher and T. Nguyen
Adv. Math., vol. 346 (2019), 665-718.

8. Structure of normally and finitely non-co-Hopfian groups
Groups Geom. Dyn., vol. 15 (2021), no. 2, 465-489.

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

6. Towers of regular self-covers and linear endomorphisms of tori
Geom. Topol., vol. 22 (2018), no. 4, 2427-2464.

5. Rigidity of convex divisible domains in flag manifolds
With A. Zimmer
Geom. Topol., vol. 23 (2019), no. 1, 171–240.

4. Quasicircle boundaries and exotic almost-isometries
With J.-F. Lafont and B. Schmidt
Ann. Inst. Fourier, vol. 67 (2017), no. 2, 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., vol. 285 (2016), no. 2, 393-426.

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

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