The Calabi Problem from a Birational Geometer's Viewpoint - Part 2

Explore the second part of a two-day Frontiers Seminar lecture series delivered by renowned algebraic geometer Carolina Araujo at the University of Miami. Delve into "The Calabi problem - from a birational geometer's viewpoint II," a 53-minute talk that continues the exploration of the Calabi problem in complex geometry. Gain insights into the challenges of determining which compact complex manifolds admit Kähler-Einstein metrics, with a focus on Fano manifolds and their positive curvature properties. Learn about the Yau-Tian-Donaldson conjecture and its resolution, connecting Kähler-Einstein metrics to K-polystability. Discover how recent advancements in birational geometry have contributed to understanding K-polystability and opened new research directions. Benefit from the expertise of Carolina Araujo, a distinguished researcher from the Instituto Nacional de Matemática Pura e Aplicada in Brazil, known for her contributions to algebraic geometry and recipient of prestigious awards including the L'Oreal Award for Women in Science and the Ramanujan Prize.