Nonabelian Mixed Hodge Structures

Explore nonabelian mixed Hodge structures in this comprehensive lecture by Carlos Simpson from the University of Nice. Delve into the foundations of this concept, developed in collaboration with Ludmil Katzarkov and Tony Pantev in the 1990s. Examine the connections to Morgan-Hain mixed Hodge structures on rational homotopy and the Malcev completion of the fundamental group. Investigate Hain's mixed Hodge structures on relative completion and their application to the local ring of character varieties. Discover how these concepts generalize to schematic homotopy types through the work of Katzarkov-Pantev-Toen and Pridham. Analyze the weights arising from noncompactness of base varieties and their relationship to parabolic structures. Gain insights into this advanced topic in algebraic geometry, presented as part of the AGNES 2023 conference at Stony Brook University.