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Explore a groundbreaking seminar on strong convergence in graph theory and random matrices. Delve into Ramon Van Handel's innovative approach to addressing Alon's conjecture and Friedman's theorem. Discover how soft arguments can lead to powerful results in understanding spectral gaps of random regular graphs. Learn about the implications of this new methodology for large deviation probabilities and high-dimensional representations of symmetric and classical groups. Gain insights into the connections between random graphs, geometry, and operator algebras. Understand the significance of this work in advancing computer science and discrete mathematics research.