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Explore the fascinating world of instanton sheaves on 3-dimensional varieties in this 50-minute lecture by Marcos Jardim from UNICAMP. Delve into the historical development of instanton sheaves, starting from the Atiyah-Ward correspondence and the ADHM construction in the 1970s, and progressing to the latest advancements involving Bridgeland stability conditions. Gain insights into the collaborative research conducted by Jardim, G. Comaschi, C. Martinez, and D. Mu as they push the boundaries of this intriguing mathematical frontier.