Computing Invariant Manifolds and Assimilating Data in Tipping Problems

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This award is made as part of the FY 2021 Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowships, MPS-Ascend Program. Emmanuel Fleurantin is awarded this fellowship to conduct a program of research and education at the Renaissance Computing Institute (RENCI) located at the University of North Carolina (UNC) at Chapel Hill in the mathematical sciences, including applications to other disciplines, under the mentorship of the sponsoring scientist Prof. Christopher K. Jones. This project will develop new computational tools concerning tipping phenomena in complex dynamical systems, such as sudden abrupt changes in a climate subsystem. Along with this research, Fleurantin will initiate training and outreach efforts to broaden participation of Underrepresented Minorities in mathematical sciences.The project will develop new theory in the mathematics behind rate and noise induced tipping through research on: 1) computations of stable/unstable manifolds of base attractors and complex basin boundaries and their connecting orbits in a compactified system with a varying rate parameter, 2) capturing the effect of noise-facilitated tipping through a most probable path connecting orbit, and 3) understanding transversality of intersections of manifolds in the complex systems arising in tipping point problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.