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Metric reconstruction from minimal surface areas
Mathematical Physics Seminar| Speaker: | Spyros Alexakis, University of Toronto |
| Location: | 918 3509 0938 Zoom |
| Start time: | Fri, Apr 2 2021, 11:00AM |
We address the following question: Consider a Riemannian 3-manifold (M^3, g) with (mean-convex) boundary. For any loop on the boundary assume we know the area of the corresponding area-minimizer. Does this information suffice to determine the metric g? We answer this in the affirmative for broad (open) sets of 3-manifolds. This question partly originates from question in the AdS-CFT correspondence, where one seeks to reconstruct the bulk space-time from knowledge of expectation values of Wilson loops that live on the boundary. We will also discuss the outlook on further generalizations of our results in this direction. Joint work with T. Balehowsky and A. Nachman.
Contact Andrew Waldron for password