Resurgence, Quantum Modularity and Quantum Invariants in Three-Manifolds
Offered By: Institut des Hautes Etudes Scientifiques (IHES) via YouTube
Course Description
Overview
Explore the intricate connections between resurgence, quantum modularity, and quantum invariants in this advanced mathematics lecture. Delve into the Witten-Reshetikhin-Turaev (WRT) quantum invariant of three-manifolds and its relation to the Chern-Simons partition function. Examine how resurgence techniques have led to significant discoveries in quantum Chern-Simons field theory, illuminating the interplay between compact and complexified gauge groups. Investigate the connection between the WRT quantum invariant and the BPS q-series invariant, including the radial limit conjecture and quantum modularity. Focus on the case of Seifert fibered homology spheres, exploring how the WRT quantum invariant determines complex Chern-Simons invariants through resurgence. Learn about recent proofs of the radial limit conjecture and quantum modularity based on resurgence formulas for the BPS q-series. Gain insights from William Mistegard's collaborative research with other mathematicians in this cutting-edge field of quantum topology and mathematical physics.
Syllabus
William Mistegard - Resurgence, Quantum Modularity and Quantum Invariants
Taught by
Institut des Hautes Etudes Scientifiques (IHES)
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