Explore a 48-minute lecture by Vatsal Sharan from the University of Southern California, presented at the Simons Institute, on the interplay between algorithms and Transformers. Delve into how algorithmic tools from optimization theory, Fourier transforms, and Boolean function analysis can illuminate the mechanisms Transformers use to tackle basic computational tasks like linear regression and addition. Examine the impact of architecture and pre-trained data on Transformers' learning processes. Discover how Transformers themselves are being utilized to innovate and design data structures for tasks such as nearest neighbor search, bridging the gap between traditional algorithms and modern machine learning approaches.