Project Grant 2400036

Award Date 7/1/24
Completion Date 6/30/27
Dollars Obligated $389K
Federal Grant Program
47.049
Assistance Type
Project Grant
Place of Performance
Amherst, MA 01003, USA
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  1. Analyze the long-term dynamics and stability of dispersive flows from a probabilistic perspective in energy subcritical regimes.
  2. Establish the invariance of Gibbs measures for the three-dimensional nonlinear Schrödinger equation, a model in constructive quantum field theory.
  3. Develop a probabilistic local theory for the hyperbolic sine-Gordon equation and examine the invariance of its Gibbs measure.
  4. Advance random tensor theory for nonlinear wave equations and non-Gaussian data.

This research aims to provide a fundamental understanding of how inherent randomness propagates in various nonlinear wave phenomena, with applications in fields such as atmospheric physics, quantum mechanics, and fiber optics. The project also supports the training of graduate students and junior researchers in these interdisciplinary areas.

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