Elliptic Curves: Theory and Applications

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Related lectures (32)

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Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Projective Geometry: Tangent Lines

Discusses the correction of tangent lines and projective plane curves, exploring topological applications and curve structure.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Directed Networks & Hypergraphs

Explores directed networks with asymmetric relationships and hypergraphs that generalize graphs by allowing edges to connect any subset of nodes.

Irreducible Polynomials: Degree and Roots

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Functional Equation of Zeta

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

Projective Plane Curves

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Equations: Degree and Solutions

Explores polynomial equations, their degree, solutions, and domain definition.

Introduction to Elliptic Curves

Covers the basics of elliptic curves, their significance in cryptography, and their applications in public key cryptography.