Master Class on Geometric Analysis on Noncompact Manifolds
In the important and internationally thriving subjects of geometric analysis and mathematical physics, a core skill for researchers is that of solving (linear) elliptic partial differential equations, e.g. static Schrödinger equations, on Riemannian manifolds, with natural geometric content. While the basic theory in the compact case is classical and can be presented very cleanly, and is indeed standard material in most advanced analysis programs, the methods in the noncompact case are harder to come by and can have a steep learning curve for beginners in the field.
In this PhD school, we thus wish to provide an invitation to the analysis of partial differential equations on noncompact Riemannian manifolds, via examples from major current research topics where these techniques are applied.