In a research statement, he says:
"The essence of arithmetic geometry lies not in the various specific schemes that occur in a specific arithmetic-geometric setting, but rather in the abstract combinatorial patterns, along with the combinatorial algorithms that describe these patterns, that govern the dynamics of such specific schemes."
Regarding this, he then talks about how his main motivations are monoids, Galois categories, and dual graphs of degenerate stable curves, which leads him to talking about his geometry of categories stuff, and then to "absolute anabelian geometry." He then links to a bunch of papers that I would assume elaborate a bit on it. He then goes on to talk about extending Teichmuller Theory.
Generally, his research statement is fairly readable (and consider that I'm very much a nonspecialist in arithmetic anything) and seems to link to things with more details.
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