Projects of a Borel Graph

A Borel graph is a mathematical structure where points (or nodes) are connected by edges based on certain rules, within a well-defined measurable space. Projects of a Borel graph involve studying how these connections can be organized, classified, or decomposed in terms of measurable sets and properties. Essentially, they analyze the ways the graph's structure interacts with measurable functions and subsets, helping mathematicians understand the complexity and behavior of such graphs in descriptive set theory and related fields. This insights can be useful in areas like logic, dynamics, and combinatorics.