Lectures related to Surfaces: The Torus

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Explores chaos in quantum field theories, focusing on conformal symmetry, OPE coefficients, and random matrix universality.

Explores the relation between resistance and force fluctuations in dissipative systems, with applications to various phenomena.

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Covers the deduction of the Lagrange formula and virtual displacements with examples of spherical slides.

Covers random walk simulation, mean displacement, and diffusion coefficient calculations for weakly ionized particles.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.