Sandra Cerrai
University of Maryland, MD·Mathematics & Statistics
Complex systems are often simplified by keeping only a few main factors. Yet effects that look tiny, such as weak random noise or slight friction, can add up and become decisive over long times.
- Fields
Mathematics & Statistics
Physics
- Topics
stochastic partial differential equations
stochastic analysis
probability theory
- Grants
- 1 known grant, through Aug 2027
What they work on
- Prove that the Smoluchowski-Kramers small-mass limit holds for stochastic damped geometric wave equations, starting with one-dimensional stochastic wave maps.
- Extend small-mass limit results to wave systems with friction that depends on the system's state, including local and non-local friction, both over finite times and for stationary solutions.
- Develop an infinite-dimensional version of Freidlin-Wentzell averaging theory for randomly perturbed partial differential equations that have conservation laws.
- Construct SPDEs that stay on level sets of conserved functionals, and prove that they have invariant measures, unique ergodicity and averaging limits.
More about the research
This mathematics project studies how fast and slow effects interact in systems with infinitely many degrees of freedom. Examples include vibrating strings or fields, described by stochastic partial differential equations (SPDEs). SPDEs are equations for quantities that vary in space and time and are pushed around by random noise. The project focuses on SPDEs with conservation laws, meaning quantities that stay fixed over time. This area is still largely unexplored in infinite dimensions.
Why it matters
The work is mainly basic mathematics. It adds to the theory of how small random and deterministic disturbances shape the long-term behavior of complex systems. The grant says these results could provide tools for studying similar multiscale effects in mathematical physics, applied mathematics and other sciences.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Le Chen
Auburn University, AL·Mathematics & Statistics·Early-career
Prove the existence of nontrivial invariant measures for the stochastic heat equation and the parabolic Anderson model, arising from the interaction between noise structure and rough initial data.
Bjoern Bringmann
Princeton University, NJ·Mathematics & Statistics
Prove that the Gibbs measure of the three-dimensional cubic nonlinear Schrödinger equation is invariant under its dynamics. This would be the first invariance result for a Gibbs measure that is critical with respect to probabilistic scaling.
Amarjit Budhiraja
University of North Carolina at Chapel Hill, NC·Mathematics & Statistics
Characterize the hydrodynamic limit of the infinite Atlas model, a rank-based particle model from stochastic portfolio theory, by linking it to Stefan-type free boundary problems, especially when particles start densely packed.
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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