In this talk, I plan to discuss how differential geometry can provide useful insights into the study of ordinary and partial differential equations. In particular, I will focus on the role of symplectic geometry in classical Lagrangian and Hamiltonian mechanics, as well as its generalization to the multisymplectic geometry of classical field theory. Finally, I will talk about how this perspective has paved the way for the development of ``geometric'' numerical integrators, which exactly preserve important structures, symmetries, and invariants.
Thursday, April 9, 2009
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9056