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Explore a one-hour quantum symmetry seminar lecture where Bin Gui, assistant professor at Tsinghua University's YMSC, delves into the relationship between Segal's sewing construction and pseudo-q-traces in vertex operator algebras. Learn how Zhu's 1990 proof demonstrated that q-traces of vertex operators for C2 cofinite rational VOA modules span a modular-invariant space, and how these relate to Segal's sewing construction. Discover Miyamoto's 2004 advancement showing the necessity of generalizing to pseudo-q-traces for C2 cofinite irrational cases, and understand how these seemingly disparate concepts can be unified through a modified interpretation of Segal's sewing framework. Examine the geometric interpretation of pseudo-q-traces and its application in proving the Gainutdinov-Runkel conjecture about torus conformal blocks and V-module categorical data. Benefit from Gui's expertise in vertex operator algebras, functional analysis, and tensor categories, developed through his academic journey from Shanghai Jiao Tong University through Vanderbilt University and Rutgers University.
