University of Copenhagen, October 9-13, 2017
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.
The confirmed main speakers, Prof. Claudio Arezzo (ICTP), Prof. Colin Guillarmou (CNRS/Univ. Paris Sud (Orsay)), and Assistant Prof. Klaus Kröncke (Hamburg Uni.) are internationally acknowledged experts in this very active field of research, and they are looking forward to sharing their extensive knowledge and experience within this exciting subject with the participants.
The workshop will be centered around advanced examples from current research. Firstly, on gluing methods for nonlinear partial differential equations, in mean curvature equations and in complex geometry (Arezzo). Also, on asymptotically hyperbolic manifolds (Guillarmou). Finally, via examples from the theory of general relativity (Kröncke).
By the end of the course, the participants will have acquired an up-to-date overview of some of the latest work in these areas and should be prepared for further study as well as embarking on research projects on their own.
Teaching and learning methods
Lectures and exercise classes.
The master class will take place at the University of Copenhagen, Denmark. Copenhagen is a beautiful harbor city, famous for being among the safest and most enjoyable places to live in the world.
The master class is organized by Niels Martin Møller and Bergfinnur Durhuus, and is supported by the Villum Centre for the Mathematics of Quantum Theory (QMATH) and the Department of Mathematical Sciences at the University of Copenhagen. QMATH is led by faculty members Jan Philip Solovej, Matthias Christandl, and Bergfinnur Durhuus, and is working in close collaboration with the Niels Bohr International Academy (NBIA).
Any questions about the master class can be directed to: QMATH@math.ku.dk