David Fisher (cv)

Milton B. Porter Professor of Mathematics

Rice University

Publications and preprints:

• 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

• Recent progress in the Zimmer program

• 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 acting on manifolds: around the Zimmer program

• Groups not acting on manifolds (with L.Silberman)

• Local Rigidity of group actions: Past, Present, Future

• Strengthening Kazhdan's Property $(T)$ by Bochner Methods (with T.Hitchman)

• $\Out(F_n)$ and the spectral gap conjecture

• 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)

• Deformations of group actions

• 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.