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Explore advanced topics in algebraic and differential geometry through this intensive mini-school featuring leading experts in the field. Delve into geometric invariant theory (GIT) stability, canonical metrics, and K-stability with comprehensive introductions and discussions of current research developments. Master the fundamentals of rational dynamics on Riemann spheres and polynomial automorphisms, while examining the geometry and dynamics of projective surface automorphisms. Investigate enumerative geometry through Gromov-Witten invariants and their connections to moduli of curves and representation theory. Study birational geometry alongside derived categories and their interconnections, gaining insights into how these powerful tools apply to geometric problems. Examine singularities from multiple perspectives, including Frobenius invariants, characteristic zero and positive characteristic connections, and analytic viewpoints. Learn about singular Hermitian metrics and their role in understanding direct images of pluricanonical sheaves and bundles, with emphasis on positivity properties and geometric applications.
