Reconstructing 3D cube complexes from boundary distances

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• Jane Tan, Oxford
• Thursday 04 May 2023, 15:00-16:00
• Arts LR6.

If you have a question about this talk, please contact Dr Richard Mycroft.

Given a quadrangulation of a disc, suppose we know all the pairwise distances (measured by the graph metric) between vertices on the boundary of the disc. Somewhat surprisingly, a result of Haslegrave states that this is enough information to recover the whole interior structure of the quadrangulation provided all internal vertex degrees are at least 4. In this talk, we look at a generalisation of this result to 3 dimensions. We show that it is possible to reconstruct cube complexes that are homeomorphic to a ball from the pairwise distances between all points on the boundary sphere as long as a certain curvature condition holds. We’ll also discuss some plausible variants that turn out to be false, and generalisations that should be true. This is joint work with Haslegrave, Scott and Tamitegama.

This talk is part of the Combinatorics and Probability seminar series.

This talk is included in these lists:

• Arts LR6
• Combinatorics and Probability seminar
• School of Mathematics events

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