To help set the mathematical stage for the workshop, I will briefly present some fundamental ideas in networks and network dynamics. I will discuss various types of networks (such as directed networks, multilayer networks, and so on), with an aim towards trying to convey what we do and don't know how to do. In this vein, I will also comment about dynamics on networks, dynamics of networks, and networks that coevolve with dynamics. I plan to use roughly half of the allotted time for my presentation slides, and I expect active discussions and audience questions for the other half. Springboarding from these discussions, we should try to set the stage for formulating interesting and concrete projects at the conclusion of the workshop.
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