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Undecidability in geometry and topology

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There is a beautiful tension in topology between positive classification theorems and negative “no-go” theorems. The positive results come from geometry, and often derive ultimately from analysis. The negative results, by contrast, come from undecidability results in logic. I’ll give a survey of the history of this tension, and mention the highlight theorems — examples include Markov’s theorem that 4-manifolds cannot be classified (on the negative side), and Perelman’s Geometrization Theorem in dimension 3 (on the positive side). I’ll then go on to describe some recent undecidability results, which limit possible computations in matrix groups. This is joint work with Martin Bridson.

This talk is part of the Applied and Computational Analysis series.

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