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Explore advanced concepts in fine-grained complexity theory through a 58-minute lecture delivered by Yinzhan Xu from MIT as part of the Logic and Algorithms in Database Theory and AI Boot Camp at the Simons Institute. Delve into intricate aspects of computational complexity, focusing on fine-grained analysis of algorithms and their running times. Gain insights into cutting-edge research and methodologies used to establish tight lower bounds for various computational problems. Enhance your understanding of the theoretical foundations that underpin efficient algorithm design and analysis in computer science.