Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Curvature bounds in the large for Lorentzian length spaces
Synthetic curvature conditions for length spaces have proven extremely useful in understanding the geometry of Riemannian manifolds and have produced a great deal of wonderful mathematics in their own right. Curvature is a local property, so it is useful to find some uniform lower bound on the size of neighborhoods where curvature conditions hold true. Without this, the conditions cannot be expected to survive any convergence process. In fact, in the case of Alexandrov geometry, which generalises a lower sectional curvature bound with triangle comparison, it can be shown that the comparison condition holding locally implies that it holds globally, allowing for very strong global results.
Recently there have been a number of efforts to create a Lorentzian analog of length spaces. So far, the construction of Kunzinger and Sämann seems the most successful. In this talk I will introduce these Lorentzian length spaces and then present joint work with Tobias Beran, Lewis Napper and Felix Rott which shows that, under reasonable causality assumptions, if a triangle comparison version of timelike lower sectional curvature bounds holds locally, it also holds globally.