Mixed Hodge Structures Attached to Hybrid Landau–Ginzburg Models

Explore the intricate world of mixed Hodge structures in this advanced mathematics lecture by Andrew Harder from Lehigh University. Delve into Shamoto's construction of mixed Hodge structures for Landau-Ginzburg models and their connection to mirror symmetry for Fano varieties. Examine the functorial properties of these structures, particularly in relation to decompositions of the potential function. Discover a new spectral sequence linking the mixed Hodge structures of different Landau-Ginzburg models and its relationship to the perverse Leray filtration. Gain insights into concrete applications of this spectral sequence in the field of algebraic geometry and mirror symmetry.