An Introduction to the Minimal Model Program for Foliations - Lecture 1

This lecture explores the Minimal Model Program for foliations, beginning with a review of the framework for surface foliations before surveying recent developments in higher dimensional projective varieties. Learn about three key cases where minimal model theory for foliations has advanced significantly: rank one foliations, co-rank one foliations, and algebraically integrable foliations. The presentation also covers the emerging concept of adjoint foliated structures, which addresses unique challenges in applying minimal model techniques to foliations. Recorded during the "Foliations, birational geometry and applications" thematic meeting at the Centre International de Rencontres Mathématiques (CIRM) in Marseille, France on February 3, 2024, this lecture serves as an introduction to how the classification framework for algebraic varieties can be adapted to study foliation structures.