Harmonic Forms and Riemann Surfaces

Related lectures (30)

Page 2 of 3

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

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

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

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.