Physics
Seminar
Wednesday,
Oct. 13, 2004, 4:30 pm
Willet Science Center 101
Jose L.
Balduz Jr.
Department of Physics
Mercer University





Modeling
Space with Simple Graphs
Attempts are currently underway to describe the emergence of continuous space
or spacetime from an underlying discrete microstructure. For example, one may
model space as arising from a graph: a countable set of nodes or locations,
together with weighted links between pairs of nodes. In the simplest case the
links are not weighted, they either do or do not exist. For a given simple
graph, we may assign a distance to each pair of nodes, then embed the nodes in
a continuous flat or curved space so that those distances are recovered. We
first consider all graphs with up to four nodes, and two distinct ways to
define the distances, based on simple counting and the graph Laplacian
propagator. In some cases a given graph can be embedded in space of a particular
dimensionality, while in some cases this is impossible. We then consider larger
graphs (complete graphs, star graphs, loops and strings, random graphs) and
cluster graphs, where cliques of tightly linked nodes become metanodes in a weighted
graph (nonlocal web). This leads us to consider hypergraphs, which may be used
to model spacetime causal sets and quantum fields.
Please join us for
light refreshments at 4:15pm outside WSC 109.