Definition of a Gibbs measures

Covers the transition from the six-vertex model to FK-percolation, focusing on critical phenomena and phase transitions in two-dimensional systems.

Explores spherical symmetry in statistical mechanics and its role in phase transitions.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.