Tropicalizing Principal Minors of Positive Definite Matrices

Explore a mathematical lecture from the Geometry of Matroid Workshop where Georgia Institute of Technology's Josephine Yu delves into the tropicalization of principal minors of positive definite matrices over real valued fields. Learn how this tropicalization creates M-concave functions on discrete n-dimensional cubes and discover its relationship with larger tropical Grassmannians and affine tropical Flag varieties within submodular cones. Examine new polynomial inequalities on principal minors and coefficients of Lorentzian polynomials through the process of lifting tropical inequalities.