Anne Wilkinson
University of Chicago, IL·Mathematics & Statistics
Why do some systems behave predictably while others react chaotically to the slightest nudge? The question bears on problems from weather forecasting to data security.
- Fields
Mathematics & Statistics
- Topics
smooth dynamics
dynamical systems
chaos
- Grants
- 1 known grant, through Jun 2028
What they work on
- Make progress on the symplectic C1 ergodic hypothesis by using new perturbation and 'blender' techniques to prove density results for stably ergodic symplectomorphisms, maps that preserve a particular geometric structure.
- Prove that minimal strong foliations, layered structures along stretching directions, are open and dense, and that their associated u-Gibbs equilibrium measures are unique, with consequences for higher statistical properties.
- Develop the 'affine centralizer program', linking the algebraic size of a diffeomorphism's centralizer to its long-term dynamics, to classify partially hyperbolic actions on nilmanifolds and other homogeneous spaces.
More about the research
Smooth dynamics studies systems that evolve by repeatedly applying a smooth rule to the points of a space. It asks when orderly or chaotic behavior appears and when it persists. This project seeks mathematical rules for how order and chaos coexist, organized around three themes: stability, typicality and rigidity.
Why it matters
This is basic mathematics. It aims to clarify when chaotic behavior is stable or typical and how geometric structures govern how systems mix over time. The project ties these questions to concerns such as weather forecasting and data security. The new techniques will be collected in a graduate book and shared through lectures and podcasts.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Adam Kanigowski
University of Maryland, MD·Mathematics & Statistics
Study how chaotic and statistical properties arise and interact in smooth dynamical systems where some, but not all, Lyapunov exponents (rates at which nearby paths spread apart) are zero.
Jason DeVito
University of Tennessee-Martin, TN·Mathematics & Statistics
Determine which homogeneous spaces and biquotients, spaces built from symmetry groups, carry a double disk bundle structure, made by gluing two disk-shaped families of disks together.
Matthew Stover
Temple University, PA·Mathematics & Statistics
Use ideas from geometry, topology, algebraic geometry and dynamics to answer open questions, including basic existence problems, about real and complex hyperbolic lattices, which are discrete symmetry groups of curved spaces.
The school
University of Chicago: 39 labs on PI Pages, $681M a year on research, 457 research doctorates a year.
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