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Nonabelian Mixed Hodge Structures

Offered By: Stony Brook Mathematics via YouTube

Tags

Algebraic Geometry Courses Fundamental Groups Courses Homotopy Theory Courses

Course Description

Overview

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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.

Syllabus

Nonabelian mixed Hodge structures - Carlos Simpson


Taught by

Stony Brook Mathematics

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