Adam Kanigowski
University of Maryland, MD·Mathematics & Statistics
Can a fully deterministic system, one whose future is completely fixed by its present state, behave as unpredictably as a sequence of independent coin tosses? This question drives the study of chaos in smooth dynamical systems.
- Fields
Mathematics & Statistics
- Topics
ergodic theory
dynamical systems
smooth dynamics
- Grants
- 1 known grant, through May 2029
What they work on
- 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.
- Measure "slow chaos" in zero-entropy dynamical systems, beyond the algebraic unipotent examples, by establishing rates of mixing and equidistribution, spectral properties and limit theorems.
- Prove sparse ergodic theorems for homogeneous dynamical systems. These describe how orbits behave when sampled along polynomial sequences and k-primes, numbers with exactly k prime factors.
More about the research
These are mathematical models of motion on curved spaces called manifolds. They connect to physics, geometry, number theory and even economics. This project combines tools from ergodic theory (the study of the long-term statistical behavior of systems), probability and geometry to build a general framework for these chaotic and statistical properties.
Why it matters
This is basic mathematics. It clarifies when deterministic systems behave randomly and how quickly they mix and spread out. The results could eventually inform related questions in geometry and number theory, such as how orbits behave along primes. They could also inform physics and economics, where chaotic dynamics model real systems.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Anne Wilkinson
University of Chicago, IL·Mathematics & Statistics
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.
Osama Khalil
University of Illinois Chicago, IL·Mathematics & Statistics·Early-career
Study how rational points are distributed near self-similar (fractal-like) sets, using homogeneous dynamics, the study of motion on spaces built from symmetry groups, to attack questions in Diophantine approximation.
Samuel Punshon-Smith
Tulane University of Louisiana, LA·Mathematics & Statistics·Early-career
Develop a microlocal framework, using pseudodifferential operators that track behavior across spatial scales, to analyze how randomly fluctuating velocity fields mix a substance in advection-diffusion and nonlinear fluid PDE models.
The school
University of Maryland: 49 labs on PI Pages, $1.5B a year on research, 602 research doctorates a year.
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