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Explore the Nahm transform's role in analyzing Yang-Mills instanton moduli spaces in this 58-minute conference talk by Mark Stern at BIMSA. Delve into the transform's origins in representation theory and discover recent advancements in extending its application to ALF gravitational instantons, based on collaborative work with S. Cherkis and A. Larrain-Hubach. Gain insights into this fundamental tool's evolution and its expanding significance in mathematical physics.