I will give a panoramic view of some of my research topics which are currently active. These include: (1) the study of communicability functions on networks and their Euclidean geometric embedding; (2) the study of time-and-space nonlocal hops in networks and the emergence of sub- and superdiffusion; (3) the study of degree-biased Laplacians on networks and the emergence of advective-diffusive processes; (4) fractional calculus approaches to network theory. These topics will then be developed in details in a series of IFISC talks to be announced.
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