Title: Network Theory
Speaker: John Baez
Abstract: Networks are important in many branches of science, from computer science and electrical engineering to biochemistry and beyond. Category theory should provide a unified approach to all these networks, and our team at UCR is working to realize this dream. Networks of a given kind can be composed by attaching the inputs of one to the outputs of another, so we can think of networks as morphisms. But we can also talk about morphisms between networks, so networks of a given kind are morphisms in a double category - and we can set two networks side by side, or "tensor" them, so this double category is symmetric monoidal. One approach to networks treats them as "structured cospans", using a formalism that is being developed by Kenny Courser and further studied by Christina Vasilakopoulou. Jade Master is applying this formalism to Petri nets, a type of network important in computer science; Adam Yassine is applying it to classical mechanics; Daniel Cicala is applying a variant to the study of graph rewriting. We can also simplify the study of networks using categories instead of double categories; Brandon Coya is using this idea to study electric circuits. Finally, Christian Williams is applying these ideas to computer programming (working with the Pyrofex Corporation) while Joseph Moeller is applying them to networks of interacting agents (working with Metron Scientific Solutions).
Tuesday, April 3 at 3:40pm to 5:00pm
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