Explore linear programming applications in geometric measure theory through this 58-minute lecture by Bala Krishnamoorthy. Delve into integral currents, simplicial flat norm, and polyhedral approximation. Examine the connections between integer programming and total unimodularity, and discover simplicial deformation techniques. Gain insights into median shapes and their illustrations while considering open questions in the field. This Applied Algebraic Topology Network presentation offers a comprehensive overview of key concepts and their practical implications in geometric measure theory.