Master Class on Geometric Analysis on Noncompact Manifolds – University of Copenhagen

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Masterclass on Geometric Analysis on Noncompact ManifoldsUniversity of Copenhagen, October 9-13, 2017

Tentative shedule

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.

Scientific content

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).

Outcome

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.

Lecturers

Location

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.

Organizers

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).

Venue

The QMATH group is located at the MATH department in the H.C. Ørsted Institute across the park. Directions to the MATH department, and several other useful locations, can be found here.

Accommodation

We recommend Hotel 9 Små Hjem, which is pleasant and inexpensive and offers room with a kitchen. Another inexpensive option is CabInn, which has several locations in Copenhagen: Hotel CityHotel Scandivania, and Hotel Express. Somewhat more expensive, and still recommended, options are Hotel Nora and Ibsen's Hotel.

Application

An on-line application is required to be able to participate in the master class.

Online application form.

The application deadline: September 17, 2017.

Participants will be selected on the basis of the applications. For PhD students, indicating the e-mail address of an academic supervisor is is required, as well as a motivated explanation of the interest in the workshop. The master class is worth 2.5 ECTS.

Contact

Any questions about the master class can be directed to: QMATH@math.ku.dk