The Calabi Problem from a Birational Geometer's Viewpoint - Part 1

Explore the intricacies of the Calabi problem from a birational geometer's perspective in this captivating lecture by renowned algebraic geometer Carolina Araujo. Delve into the fascinating world of complex manifolds and Kähler-Einstein metrics as Araujo presents an overview of this formidable problem at the intersection of differential and algebraic geometry. Discover the historical context, including Calabi's 1954 ICM lecture, and learn about the significant breakthroughs made by Yau and Aubin in the 1970s. Examine the challenges posed by Fano manifolds with positive curvature and understand the importance of the Yau-Tian-Donaldson conjecture. Gain insights into how tools from birational geometry have revolutionized the investigation of K-polystability, leading to remarkable progress in the field. This lecture, delivered by a world-renowned expert and recipient of numerous prestigious awards, offers a unique opportunity to explore cutting-edge developments in algebraic geometry and their profound implications for both differential and algebraic geometry.