Bjoern Bringmann
Princeton University, NJ·Mathematics & Statistics
Picture a lake on a windy day. Its waves never stop moving, yet the surface looks about the same from minute to minute, because averages such as wave height and speed stay constant.
- Fields
Mathematics & Statistics
Physics
- Topics
Gibbs measures
invariant measures
nonlinear Schrödinger equation
- Grants
- 1 known grant, through Jun 2028
What they work on
- 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.
- Establish well-posedness of the stochastic wave maps equation, a randomly forced geometric wave equation, by combining methods from partial differential equations, probability theory, and differential geometry.
- Prove global well-posedness of the stochastic Yang–Mills–Higgs heat flow in two dimensions and use it to rigorously construct two-dimensional Yang–Mills–Higgs measures from Euclidean quantum field theory.
More about the research
Mathematicians and physicists describe this kind of "statistical equilibrium" with Gibbs measures, which assign probabilities to all possible states of a system. Gibbs measures matter in condensed matter physics, plasma physics, and quantum field theory. The hard mathematical question is how the randomness described by a Gibbs measure evolves as the system follows its equations of motion. For example, how likely is it that several small waves merge into one large wave? The work combines partial differential equations (PDEs), probability theory, and differential geometry to tackle open problems of this kind.
Why it matters
This is fundamental mathematics. It aims to put the statistical behavior of physical systems, from water waves to quantum fields, on rigorous footing by explaining how randomness evolves under wave and heat equations. The results could eventually inform models in condensed matter physics, plasma physics, and quantum field theory. They could also build new links between analysis, probability, and geometry.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Sandra Cerrai
University of Maryland, MD·Mathematics & Statistics
Prove that the Smoluchowski-Kramers small-mass limit holds for stochastic damped geometric wave equations, starting with one-dimensional stochastic wave maps.
Svetlana Jitomirskaya
University of California-Berkeley, CA·Mathematics & Statistics
Develop non-perturbative Green's function estimates for lattice quasiperiodic operators when the frequency parameter is restricted to a submanifold of a torus.
Sung-Jin Oh
University of California-Berkeley, CA·Mathematics & Statistics·Early-career
Prove a forward-in-time scattering criterion for initially outgoing solutions of the energy-critical wave maps and hyperbolic Yang-Mills equations, as a step toward the soliton resolution conjecture in the one-soliton regime.
The school
Princeton University: 26 labs on PI Pages, $559M a year on research, 403 research doctorates a year.
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