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Lecture
Building surfaces from equilateral triangles
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Related lectures (30)
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.
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.
Harmonic Forms: Main Theorem
Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.
Open Mapping Theorem
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Proper Actions and Quotients
Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.
Meromorphic Functions & Differentials
Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Holomorphic Functions: Taylor Series Expansion
Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.
Harmonic Forms and Riemann Surfaces
Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.
Conformal Blocks: Functions on Moduli Spaces
Covers conformal blocks and their significance in complex structures and moduli spaces.
Modular Curves: Genus and Mapping Theorems
Explores holomorphic maps, ramification points, and the genus of a modular curve.
Modular curves: Riemann surfaces and transition maps
Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.
Surface Integrals: Regular Parametrization
Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.
Riemann Surfaces: Complex Manifolds
Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.
Differential Forms Integration
Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.
Introduction to Quantum Chaos
Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.
Remeshing
Explores remeshing in geometric computing, emphasizing equal edge lengths and valence close to 6.
Homology of Riemann Surfaces
Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.
Modular Forms: Dimension Formula
Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.
Geometric Proportions: Euclidean Elements
Explores geometric proportions, commensurability, and triangle construction in Euclidean geometry.
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