Nonlinear Spaces from Linear Spaces - A Matroid Theory Perspective

Join a workshop lecture from the Harvard Center of Mathematical Sciences and Applications where Federico Ardila from San Francisco State University explores the fascinating relationship between linear and nonlinear spaces through matroid theory. Discover how matroid theory serves as a combinatorial model for linearity while extending beyond linear applications. Learn how a linear subspace V of an n-dimensional vector space generates a matroid M(V) on the set {1,...,n}, and explore how this matroid contains information about related nonlinear geometric spaces. Examine specific examples that demonstrate how studying these nonlinear spaces provides new insights into matroid theory, creating a reciprocal relationship between linear and nonlinear mathematical structures.