I gave a talk at the undergraduate mathematics colloquium on interactive proofs. The notes I prepared for myself are here.

This is a way of saying that I’m still alive, even if I haven’t had time to update this blog recently! My interests have been getting more and more homotopical in nature. I’ve been thinking about the cotangent complex, which is a non-abelian example of a derived functor—you derive the functor of Kahler differentials, defined on the (nonadditive) category of algebras over a ring. The way to do this is to use Quillen’s language of model categories. The key point is that if you derive an additive functor by taking a projective resolution, which is a cofibrant replacement in some model structure on the category of chain complexes, then naturally you should derive a non-additive functor by taking a cofibrant replacement in the category of simplicial whatever. Say, simplicial algebras over a ring. I’m hoping to be able to blog about the cotangent complex in a few days.

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