The Geometry of Geometries - Matroid Theory, Old and New

Explore the fascinating world of matroid theory in this 46-minute lecture by Federico Ardila for the International Mathematical Union. Delve into the origins of matroids in linear algebra and graph theory, and discover their deep connections to various mathematical areas including field theory, matching theory, submodular optimization, Lie combinatorics, and total positivity. Examine how matroids capture the shared combinatorial essence across different mathematical settings. Learn about recent advancements in the field, focusing on three geometric models of a matroid: the matroid polytope, the Bergman fan, and the conormal fan. Gain insights into the growing geometric roots of matroid theory and their new applications. Access accompanying slides for visual support and deeper understanding of the concepts presented.