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Explore a 55-minute mathematics conference talk examining the KSBA moduli space of stable pairs, focusing on its application to log Calabi-Yau surfaces. Delve into the groundbreaking work that proves the Hacking-Keel-Yu conjecture, which suggests that for stable pairs with log Calabi-Yau varieties and ample divisors, the KSBA moduli space is toric up to finite cover. Learn how this mathematical framework, developed by Kollár-Shepherd-Barron and Alexeev, extends the moduli space of stable curves to higher dimensional varieties. Discover the intersection of minimal model program, log geometry, and mirror symmetry through collaborative research presented at the Centre International de Rencontres Mathématiques in Marseille, France. Access this enriched presentation through CIRM's Audiovisual Mathematics Library, complete with chapter markers, keywords, abstracts, and comprehensive mathematical classifications for enhanced learning and reference.
