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Explore the intricacies of spectral statistics in random regular graphs through a 42-minute lecture delivered by Harvard University's Horng-Tzer Yau at the Fields Institute. Delve into advanced mathematical concepts and their applications in graph theory, gaining insights into the latest research in this field. Scheduled for August 15th, 2024, as part of the FFFM-2024 program, this talk promises to offer valuable knowledge for mathematicians, computer scientists, and researchers interested in graph theory and spectral analysis.