M/E23

Existential definability of subsets of fields, in particular of subrings, has been studied since the 1940'ies, and has seen several applications to problems of existential decidability (generalising Hilbert's 10th Problem). To establish existential definability of valuation rings, quadratic forms often play a substantial role. In this talk, we illustrate the connection between existential definability and quadratic form theory by giving some historical examples, and then discuss a recent result relying on modern developments in quadratic form theory, like a local-global principle for function fields over complete valued fields.

Nicolas Daans

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