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We explore the mathematical foundations of plasma confinement and nonlinear dynamics for next-generation fusion reactors.
Introduction of Laboratory
We investigate the fundamental mathematical structures underlying plasma physics—an arena where the most complex systems in nature emerge. We explore challenging problems such as Grad's conjecture, kinetic theory, noncanonical Hamiltonian mechanics, relativistic statistical mechanics, and dynamo theory. We engage with nonlinear partial differential equations, which not only describe plasma behavior but also connect to broader mysteries in mathematics and physics. From the dynamics of fusion plasmas to the structure of spacetime in quantum gravity, our work touches on problems of practical and foundational significance. We view plasmas as a laboratory for discovering new geometric, analytic, and statistical principles. We aim to illuminate hidden symmetries, understand the limits of equilibrium, and develop unified frameworks for high-dimensional nonlinear dynamics. These problems link fusion energy, mathematical physics, and field theory. By solving them, we open gateways to new discoveries in mathematics and theoretical physics.
Career Summary
National Institute for Fusion Science