Yuji Hirota
Lie algebroid symmetry with bundle-valued $n$-plectic geometry
The theory of momentum maps is central in studying spaces with symmetry and has developed in various directions. Following the discovery of symmetries arising from Lie algebroids, the need to understand the classical notion of momentum maps in a unified framework has further increased. The notion of homotopy momentum sections is one of such frameworks.
In this talk, we introduce the fundamentals of homotopy momentum sections and geometry associated with it, known as bundle-valued $n$-plectic geometry. Moreover, we shall provide the relationship with quaternionic Kähler momentum maps, and shall briefly discuss a reduction theorem analogous to the Marsden-Weinstein reduction in symplectic geometry.
