Appears in collection : 2023 - T2 - WS2 - Higher structures in enumerative geometry

Give a Gorenstein Calabi-Yau curve X, the moduli stack of bounded complexes of vector bundles on X admits a 0-shifted Poisson structure. For the component that is a G_m gerbe over a smooth scheme, the 0-shifted Poisson structure descends to an ordinary Poisson structure on its coarse moduli scheme, which we call a “modular Poisson structure”. In this talk we will survey some recent progress on the study of the modular Poisson structures. In particular we will give the example when X is the Kodaira cycle, where we establish a correspondence between certain torus orbits of vector bundle stack and projected open Richardson varieties on grassmannian via modular Poisson structure.