Explore the final part of a three-part lecture series on Quillen metrics and applications, delivered by J.M Bismut from Université Paris Saclay. Delve into the fascinating world of gauged maps, vortices, and their moduli. Gain insights into historical comments and various applications, including coolant matrix, analytic torsion, and modular forms. Examine proofs utilizing both analytic and BCOV torsion, and identify key statements to watch for. Discover essential analytic tools and explore the concept of invisible paper. Conclude with a discussion on numerical invariance in this comprehensive 47-minute presentation by NCCR SwissMAP.