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Explore the existential definability of henselian valuation rings within their fields of fractions in this mathematical lecture from the Hausdorff Center for Mathematics. Delve into the classification of such valuation rings in equal characteristic through first-order properties of their residue field, following a parallel story to previous work in the field. Examine key ingredients, concrete examples, and current open questions in this area of algebraic geometry and model theory. Learn about research findings based on collaborative work with Arno Fehm and Philip Dittmann, working within the language of rings and sometimes allowing parameters. Gain insights into the theoretical framework that connects valuation theory with definability questions in mathematical logic.
