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Explore a mathematical proof of Witten's asymptotic expansion conjecture for Witten-Reshetikhin-Turaev (WRT) invariants of Seifert fibered homology spheres through resurgence theory. Learn about the primary methodology involving resurgent analysis of the Gukov-Pei-Putrov-Vafa (GPPV) invariant, a complexification of the WRT invariant, and discover how this analysis characterizes flat connections corresponding to Stokes terms while distinguishing between SU(2) and SL(2,R) connections. Examine related findings including how the radial limit of the GPPV invariant recovers the WRT invariant, the quantum modularity property of the GPPV invariant, and its relationship to the Habiro element. Gain an introduction to resurgence theory fundamentals before delving into detailed technical discussions of the underlying mathematical framework, with comprehensive background and elaboration on the proof methodology presented by researcher Yong Li from BIMSA.
