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.

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.

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.

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.

Trigonometric Functions: Right Triangle MOOC: Trigonometric, Logarithmic and Exponential Functions

Introduces trigonometric functions in right triangles, exploring angles, ratios, and special values.

Elementary Operations in Geometry

Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.

Bounding the Poisson bracket invariant on surfaces

Covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny.

Euclidean Geometry Fundamentals

Introduces the fundamentals of Euclidean geometry, covering equilateral triangles, symmetries, radical axes, and ancient architectural figures.

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