Algebraic topology and distributed computing.

I gave a seminar talk on [1].

This paper doesn’t do it (but Rajsbaum’s MSRI talk did), but the result can be reformulated combinatorially, so that the algebraic topology appears as an instance of Sperner’s lemma; this is the sort of thing that should be done at mathcamp.

Here is something that amuses me, but I know that if anyone else said it, I would find it extraordinarily annoying: seeing as these results apply to anything (I mean, the local model of computation is irrelevent), this is an example of how deterministic systems, when combined with each other, yield non-deterministic results (though I have to be careful what I mean by “deterministic”—the system as a whole is determined, but non-deterministic from the perspective of the agents in that they cannot determine the outcome). Clearly I should write a philosophy paper, called “Free will and algebraic topology: a primer,” in which people are vertices in the simplicial complex of all possible worlds.

It will be better for all of us if I stop now.