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Explore noncommutative spectra in this lecture by Ludmil Katzarkov from the University of Miami and IMSA. Delve into examples and applications of nonrationality questions, building upon the short course by M. Kontsevich. Examine potential generalizations and gain insights from joint works with Kontsevich and Pantev. Enhance your understanding of advanced mathematical concepts in this hour-long presentation delivered on January 19, 2021.