An Introduction to Rough Geometry (with a view to Euclidean Gravity)
- October 14 (Fri) at 14:00 - 16:30, 2022 (JST)
- Dr. Christy Koji Kelly (Special Postdoctoral Researcher, iTHEMS)
- Hybrid Format (Common Room 246-248 and Zoom)
- Keita Mikami
The mathematical formulation of Einstein gravity typically utilises differentiable manifolds as models of smooth spacetimes. In many scenarios, however, it is desirable to have coarser models of spacetime and a correspondingly rough theory of geometry applicable to these coarser spacetime structures. In 2D Euclidean quantum gravity, for instance, the use of Regge calculus allows one to treat triangulations as regularisations of smooth spacetimes. There has been much recent progress in the mathematical (rigorous) understanding of this theory which we briefly review. We also introduce a rich alternative framework for the study coarse Euclidean geometry in the form of metric geometry augmented by optimal transport theory. In particular we introduce several optimal transport theoretic curvatures and demonstrate that these recover the familiar smooth notions under suitable limits.
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