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Explore a comprehensive lecture on surface quotient singularities and big cotangent bundles presented by Dr. Bruno de Oliveira at the University of Miami. Delve into the hyperbolic properties of surfaces with big cotangent bundles and their connection to the Green-Griffiths-Lang conjecture. Examine a bigness criterion for resolutions of orbifold surfaces and its application to the canonical model singularities criterion for surfaces of general type. Compare this criterion with other known criteria, such as the Rouseau-Rolleau criterion, and understand its analytical-based invariant for surface singularities, with calculations provided for A_n singularities. Investigate the application of this criterion to determine the minimal degree for which the deformation equivalence class of a smooth hypersurface in P^3 has a representative with big cotangent bundle.
