Baker-Bowler Theory for Lagrangian Grassmannians

Explore advanced mathematical concepts in this 57-minute lecture from the Geometry of Matroid Workshop, where Donggyu Kim from Korea Advanced Institute of Science and Technology presents groundbreaking research extending Baker-Bowler theory to Lagrangian Grassmannians. Delve into how the Grassmannian can be defined over a tract, examining the unification of theories for matroids over partial fields, valuated matroids, and oriented matroids. Learn about the parameterization of Lagrangian Grassmannian into projective space and discover the simplified list of quadrics induced by Laplace expansions. Understand the development of antisymmetric matroids, their cryptomorphic definition, and their relationship with Baker-Bowler theory. Examine the application of this framework to hyperfields, including tropical and sign hyperfields, while exploring the homotopy theorem for graphs associated with antisymmetric matroids and the significance of 3-/4-term quadratic relations in Lagrangian Grassmannian.