Theron Hitchman

Research

I am interested in rigidity properties for discrete subgroups of semisimple Lie groups, with an emphasis on rigidity of actions of these groups on compact manifolds. I am also beginning to look at some other questions in homogeneous dynamics and geometry. My work has connections to differential geometry, dynamical systems, number theory, foliations, geometric group theory and other areas.

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Papers

1. Deformation Rigidity for Toral actions of lattices in real rank one Lie groups, arXiv, submitted.
2. with David Fisher, Cocycle Superrigidity and Harmonic Maps with Infinite-Dimensional Targets.
International Mathematics Research Notices, vol. 2006, Article ID 72405, 19 pages, 2006. Journal arXiv
This is an announcement for next few items.
3. with David Fisher, Strengthening Kazhdan´s Property (T) by Bochner methods, arXiv
4. with David Fisher, Harmonic Maps into Infinite Dimensional Manifolds and Cocycle Superrigidity, in preparation.
5. with David Fisher, Local Rigidity via cohomology vanishing, in preparation.
6.with Alexander Gorodnik and Ralf Spatzier, Regularity of Conjugacies of Algebraic Actions of Zariski Dense Groups, in preparation
7. with Robin Forman, Heather Hardway, Timothy Burke, and Diane Shao, A robust and stable two protein switch: a model for the drosophila Hunchback-Bicoid system, in preparation