This project will be the next step, which is computing the scalar curvature (aka the Ricci scalar).
Expected deliverables:
A function or property for computing the scalar curvature given a causal graph.
A corresponding documentation page that can also be turned into a community post for the summer school.
Motivations
To understand how General Relativity might be related to graph rewriting, we need to understand how to extract geometric properties from graphs. This project will be part of that effort.
Approaches for computing scalar curvature already exist in Causal Set Theory (see arXiv:1001.2725, also Wiki).
Required future SetReplace features
We need a property for computing causal graphs in Yellowstone (a SetReplace redesign we are currently working on). However, this project can be implemented as a separate function, for which everything is ready.
The project goal
Thanks to @SantiagoGiner from 2021 Winter School, we now have a way of computing
CausalDensityDimension(aka Myrheim–Meyer dimension) of causal graphs.This project will be the next step, which is computing the scalar curvature (aka the Ricci scalar).
Expected deliverables:
Motivations
To understand how General Relativity might be related to graph rewriting, we need to understand how to extract geometric properties from graphs. This project will be part of that effort.
External prerequisites
SetReplace prerequisites
Difficulty
Given that approaches for doing this already exist in Causal Set Theory, this should not be too difficult to implement.
Potential instructors
@maxitg
Existing work
CausalDensityDimension(aka Myrheim–Meyer dimension) is already implemented.Required future SetReplace features
We need a property for computing causal graphs in Yellowstone (a SetReplace redesign we are currently working on). However, this project can be implemented as a separate function, for which everything is ready.