Graphs, Groups and Bell inequalities

A Bell inequality is obeyed by probabilities originating from a local, hidden-variable theory, but it can be violated by quantum probabilities. There are an infinite number of such inequalities, and they can be reformulated in terms of winning probabilities for nonlocal games. Two methods will be presented for generating new Bell inequalities. One is based on graphs, and properties of the graph, in particular its independence number and Lovasz number, provide useful information about the resulting inequality. The other is based on groups. We will show how different groups lead to nonlocal games with different structures.