Nonexpanding attractors: conjugacy to algebraic models and classification in 3-manifolds. Ergodic Theory and Dynamical Systems, 31 (2011), 719-739. Coveney.Ĭonstraints on dynamics preserving certain hyperbolic sets. Boghosian, Jonas Lätt, Hui Tang, Luis M. Philosophical Transactions of the Royal Society A, 369 (2011), 2345–2353. Unstable periodic orbits in the Lorenz attractor. Smooth stabilizers for measures on the torus. Smoothness of stable holonomies inside center-stable manifolds. Joint with Lucas Backes and Clark Butler. Of Lyapunov exponents for cocycles with invariant holonomies. 30 (2017), 1055–1132.Īn earlier (permanent preprint) version which assumed some positivity of entropy and is somewhat less technical is here. Measure rigidity for random dynamics on surfaces and related skew products. One novelty of our approach is that unlike most results in the literature we do not assume the existence of an invariant measure for the action. Assuming the action is Anosov, we then show the action is smoothly conjugate to an affine action. We study actions of higher-rank lattices on tori and nilmanifolds and show under suitable lifting conditions that the action is topologically conjugate to an affine action. Titles: Upper School Mathematics Teacher. Joint with Federico Rodriguez Hertz and Zhiren Wang. Hathaway Brown faculty do more than teach girls to learn for life theyve designed distinguished academics. Global smooth and topological rigidity of hyperbolic lattice actions. The formulas are a critical ingredients in the two papers above. Zimmer's conjecture for actions of \(\mathrm^d\)-actions. Hopkins, Michael George Putnam Professor of Pure and Applied Mathematics. Faculty Counselor / Graduation and Articulation Coordinator. We prove Zimmer's conjecture for actions of general lattice subgroups in \(\mathbb R\)-spit simple Lie groups. Harris, Joe Higgins Professor of Mathematics. Joint with David Fisher and Sebastian Hurtado. Zimmer's conjecture for non-uniform lattices and escape of mass. More details can be found in my Research Statement. Rigidity questions and problems related to the rigidity of lattice actions and the Zimmerĭescriptions of some recent papers and current projects are below. The Surface Subgroup Theorem and the Ehrenpreis conjecture. Bounds for Bounded-Primitive Renormalization. Research Emphasis: Hyperbolic Geometry, Teichmuller theory, and Dynamics of one complex variable. In particular, I am interested in measure Professor of Mathematics at the Brown University. I often apply tools from smooth dynamics and smooth ergodic theory to study rigidity phenomenon for actions of large groups.
My recent work focuses on smooth group actions. Previously, I was an Assistant Professor and a Dickson Instructor at the University of Chicago, an NSF postdoc at the Pennsylvania State University, and a graduate student at Tufts University.Ĭurriculum Vitae My C.V. I am an Associate Professor in the Mathematics Department at Northwestern University.
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