In this talk, we will introduce the Yang-Mills-Higgs-Schrödinger (YMHS) flow, which is the infinite dimensional Hamiltonian flow of the Yang-Mills-Higgs functional defined on a holomorphic fiber bundle. It originates from the Schrödinger-Chern-Simons system and naturally extends the Schrödinger map flow introduced by Ding-Wang to a gauged setting. We will discuss its geometric structures and also local well-posedness. This is a joint work with Bo Chen.
