Milton B. Porter Professor of Mathematics
Rice University
Seminars I organize at Rice: Analysis and Geometry (We do not currently have a dynamics seminar, but talks on dynamics occur in both of these.)
Coming Soon: Analytic Group Theory Themester Fall 2026 at Lodha Institute Mathematical Science Institute (Mumbai).
Publications and preprints:
Finiteness of totally geodesic hypersurfaes (with Simion Filip and Ben Lowe)
Greenberg-Shalom's Commensurator Hypothesis and Applications (with N.Brody, M.Mj and W van Limbeek)
Commensurators of normal subgroups of lattices (with M. Mj and W. van Limbeek)
A fibered Tukia theorem for nilpotent Lie groups (with T. Dymarz and X. Xie)
A Tukia-type theorem for nilpotent Lie groups and quasi-isometric rigidity of solvable groups (with T. Dymarz and X. Xie)
Arithmeticity, superrigidity and totally geodesic submanifolds of complex hyperbolic manifolds (with U. Bader, N. Mller and M.Stover)
Smooth and analytic actions of $SL(n,{\bf R})$ and $SL(n,{\bf Z})$ on closed $n$-dimensional manifolds (with K. Melnick)
A new proof of finiteness of maximal arithmetic reflection groups (with S. Hurtado)
Zimmer's conjecture for non-uniform lattices and escape of mass (with A. Brown and S. Hurtado)
Rigidity, lattices and invariant measures beyond homogeneous dynamics
Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T) (with A. Brown and S. Hurtado)
Arithmeticity, Superrigidity, and Totally Geodesic Submanifolds (with U. Bader, N. Mller and M.Stover)
Zimmer's conjecture for actions of $\mathrm{SL}(m,\mathbb{Z})$ (with A. Brown and S. Hurtado)
Superrigidity, arithmeticity, normal subgroups: results, ramifications and directions
Finiteness of Maximal Geodesic Submanifolds in Hyperbolic Hybrids (with J.Lafont, N.Miller and M.Stover)
Rigidity of warped cones and coarse geometry of expanders (with T. Nguyen and W. van Limbeek)
Quasi-Isometric Embeddings of Symmetric Spaces (with K.Whyte)
Quasi-isometric embeddings of non-uniform lattices (with T. Nguyen)
Character varieties and actions on products of trees (with M. Larsen, R. Spatzier and M. Stover)
Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds (with B.Kalinin and R.Spatzier)
Coarse differentiation of quasi-isometries II: Rigidity for Sol and Lamplighter groups (with A.Eskin and K.Whyte)
Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs(with A.Eskin and K.Whyte)
Cross-wired lamplighter groups (with Y.Cornulier and N. Kashyp)
Totally non-symplectic Anosov actions on tori and nilmanifolds (with B.Kalinin and R.Spatzier)
Groups not acting on manifolds (with L.Silberman)
Strengthening Kazhdan's Property $(T)$ by Bochner Methods (with T.Hitchman)
Cocycle superrigidity and harmonic maps with infinite dimensional targets (with T.Hitchman)
Quasi-isometries and rigidity of solvable groups (with A.Eskin and K.Whyte)
Local rigidity of affine actions of higher rank groups and lattices (with G.Margulis)
Continuous quotients for lattice actions on compact manifolds (with K.Whyte)
Non-ergodic actions, cocycles and superrigidity (with D. Witte Morris and K.Whyte)
Nonexistence of invariant rigid structures and invariant almost rigid structures (with J.Benveniste)
Almost isometric actions, property $(T)$, and local rigidity (with G.Margulis)
When is a group action determined by its orbit structure? (with K.Whyte)
Local Rigidity for Cocycles (with G.A.Margulis)
On the arithmetic structure of lattice actions on compact spaces.
Rigid geometric structures and representations of fundamental groups.
Geometric lattice actions, entropy and fundamental groups. (with R.Zimmer)
A canonical arithmetic quotient for actions of lattices in simple groups.