We are entering the Anthropocene, a new geological epoch in which the biosphere is strongly affected by human activities. Thus, just as 20th-century mathematics drew inspiration from physics, we can expect 21st-century mathematics to draw inspiration from biology, ecology and the environmental problems that confront us. What do category theorists, of all people, have to say about this? Researchers in many fields draw diagrams of networks: flow charts, electrical circuit diagrams, signal-flow graphs, Bayesian networks, Feynman diagrams and the like. In principle these diagrams fit into a common framework: category theory. But we are still far from a unified theory of networks. We give an overview of the theory as it stands now, with an emphasis on topics for future research, some involving higher categories.
You can see the slides here.
For a series of videos and slides covering different aspects of network theory, try:
To read more about the network theory project, go here: