Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, September 28, 2021, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room and maybe CAB G51

Speaker: Valentin Stoppiello

Edge sets of three dimensional triangulations

In my master thesis, we look at triangulations and subdivisions in three dimensions from different perspectives, to learn more about the structure of the space of triangulations. The main topic of the talk is about representing three-dimensional triangulations as Boolean strings. This representation follows from the observation that triangulations in three dimensions are uniquely characterised by their edge sets. We prove that when giving the flip graph a suitable orientation, it is an induced subgraph of the Boolean lattice. Additionally, we calculate an upper bound for the maximal length of directed paths in this subgraph, and show that it is tight.

These results are from my master thesis "Triangulations and Subdivisions in three dimensions", supervised by Emo Welzl, Patrick Schnider and Nicolas Grelier.

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