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Explore advanced mathematical concepts in this lecture from the Geometry of Matroid Workshop where Matt W Larson from the Institute for Advanced Study delves into the geometric construction and properties of delta-matroids. Learn about the extension of matroid-related geometric constructions to delta-matroids, with particular focus on "type B" and "type C" analogues. Discover new findings on the ultra log-concavity of independent sets within delta-matroids, including previously unknown inequalities applicable to matroids. Gain insights from collaborative research conducted with Chris Eur, Alex Fink, and Hunter Spink that advances our understanding of these complex mathematical structures.