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Lecture
Harmonic Forms and Riemann Surfaces
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Related lectures (30)
Harmonic Forms: Main Theorem
Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.
Differential Forms Integration
Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Meromorphic Functions & Differentials
Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.
Holomorphic Functions: Taylor Series Expansion
Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Open Mapping Theorem
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Local Homeomorphisms and Coverings
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Hadamard Factorisation
Covers the Hadamard factorisation theorem for entire functions of order at most 1.
Applications of Residue Theorem in Complex Analysis
Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.
Proper Actions and Quotients
Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.
Complex Integration and Cauchy's Theorem
Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.
Curves with Poritsky Property and Liouville Nets
Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.
Riemann Surfaces: Complex Manifolds
Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.
Preliminaries in Measure Theory
Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.
Modular Forms: Dimension Formula
Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.
Functional Equation of Zeta
Covers the functional equation of zeta function and Jensen's formula in complex analysis.
Fundamental Solutions
Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.
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