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Explore a one-hour lecture from the BIMSA-Tsinghua Quantum Symmetry Seminar featuring Francis Bonahon from the University of Southern California, delving into the fascinating world of G-skein modules in 3-dimensional manifolds. Learn about the fundamental concepts of Witten's interpretation of quantum knot invariants within topological quantum field theory, with particular focus on the special linear group SL_n. Discover the intriguing "invisibility" property that emerges when the parameter q is a root of unity, allowing certain skein elements to be traversed without affecting the total skein. Examine the construction of these invisible elements through classical theory of symmetric polynomials in n variables. Gain insights from Bonahon, a distinguished French mathematician known for his expertise in low-dimensional topology and hyperbolic geometry, particularly in geometric structures on 3-dimensional manifolds and Teichmüller spaces.
