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Explore the fascinating mathematical landscape of Fano varieties through this comprehensive lecture delivered at the International Congress of Basic Science 2025. Delve into the fundamental concepts and advanced theories surrounding Fano geometry, a central area of algebraic geometry that studies smooth projective varieties with ample anticanonical bundles. Learn about the classification problems, birational geometry aspects, and recent breakthrough results in the field from one of the leading experts who has made significant contributions to higher-dimensional algebraic geometry. Discover the connections between Fano varieties and other areas of mathematics, including the minimal model program, K-stability, and moduli theory. Gain insights into current research directions and open problems that continue to drive innovation in this rich mathematical domain.
