Twistor Space for Moduli of Local Systems on Open Curves

Explore the construction of Deligne-Hitchin twistor spaces for moduli of framed local systems on open curves in this 58-minute conference talk by Carlos Simpson from the University of Nice. Delve into the intricacies of harmonic bundles and their role in creating preferred sections. Examine the normal bundle of a preferred section and its natural mixed twistor structure with weights 0, 1, and 2. Understand how the weight 2 piece corresponds to changes in parabolic structure. Learn about the completion process along a preferred section and its implications for the complete local ring of the moduli space of local systems at smooth points. This talk, part of the "Periods, Shafarevich Maps & Applications" conference at the University of Miami, offers a deep dive into advanced mathematical concepts at the intersection of algebraic geometry and complex analysis.