Abstract
Hodge Theory is a milestone bridging differential geometry and algebraic topology. It studies certain functions (called forms) on data rather than data points themselves, and brings an optimization perspective to decompose such functions adaptive to the underlying topology. Recently Hodge Theory inspires rising applications in computer vision, multimedia, statistical ranking, game and voting theory, in addition to traditional applications in mechanics etc. In this talk we give an introduction to Hodge Theory with examples in these applications.