Reconstructing 3D Cube Complexes from Boundary Distances

Start Date: May 3, 2023
Event Start Time: 12:15 PM
Event End Time: 1:15 PM
Seminar Series: Graduate Combinatorics Seminar
Presenter(s): Jane Tan - University of Oxford
Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
Presentation Type: Stand Alone Presentation
Abstract:
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. This is a fun result that ties together graph theory with some topology and metric geometry. 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 seminar is presented in the Grad Lounge at 12:15 via zoom.

Zoom Info:

Meeting Room ID: 917 6366 3688
Password: gcs2023

Link: https://rutgers.zoom.us/j/91763663688?pwd=NjZzTWh0M01jcXBVcFpZUndSMDJzZz09

Events