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The summer school on (CU Boulder, July 29 - August 2, 2024) will explore new developments at the intersection of condensed matter physics, C*-algebraic quantum mechanics and algebraic topology. It is organized by Agnès Beaudry (CU Mathematics), Mike Hermele (CU Physics), Markus J. Pflaum (CU Mathematics), and Daniel D. Spiegel (UC Davis).