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Organizers:

**Charles Keeton**, Rutgers University

**Arlie Petters**, Duke University

**Marcus Werner**, Kyoto University

The propagation of light probes the fundamental structure of spacetime, and its gravitational dynamics are described by general relativity or possible modifications. These theoretical models are increasingly testable thanks to the latest advances in astronomy. We will explore the mathematical properties of gravitational lensing, which is the study of how gravity acts on light. Given the remarkable recent insight that gravity theories can be constructed “geometrodynamically” so as to ensure predictivity, we will also investigate how such theories may be tested. The attractive nature of this research is that it intersects with several core areas of mathematics, e.g., differential geometry, analysis, PDEs, algebra, and probability theory.

Our interdisciplinary summer conference will be aimed at newcomers to the field, with a strong focus on team-based collaborative work. Pedagogically, the expressway into the subject is to use the thin-screen, weak-field limit of gravitational lensing, which is rich with examples that carry many of the key ideas and theorems in the field. Teams will analyze specific examples that lead to open problems. Extending beyond the weak-field limit, an accessible introduction to the relevant aspects of Riemannian, Lorentzian, and Finslerian geometry will be given, so that the differences among the three, as well as the ways in which they appear in general relativity and gravitational lensing, can be appreciated. This will lead naturally to recent results and open problems in constructive gravity and optical geometry.

This conference addresses the following topics: deterministic and stochastic weak-field gravitational lensing; numerical aspects of gravitational lensing with astrophysical applications; constructive gravity; optical geometry of Lorentzian spacetimes; non-Lorentzian optical geometries; singularities in gravitational lensing; testing five-dimensional modified gravity.

We seek an academically excellent and diverse group of peri-doctoral mathematical scientists with an interest in applications as well as physicists keen on mathematical structure.

The application period is closed. No further applications will be accepted.

- Erik De Amorim
- Nishanth Gudapati
- Nicole Hudson
- Sophia Jahns
- Michael Maroun
- Sousuke Noda
- Saulo Orizaga
- Sean Perry
- Henri Roesch
- Jessica Stewart Kelly

Further information for 2018 participants

For further information, please contact the** Associate Executive Director **at aed-mps@ams.org.