Elliptic Curves: Theory and Applications

Related lectures (32)

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

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Covers the concept of degree in homotopy theory and the structure of complexes with two simplices.

Covers the fixed points of the Ruelle-Thurston operator and its applications in complex analysis.

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Introduces Galois fields, elliptic curves, factorization algorithms, and the discrete logarithm problem in cryptography.

Explores isogeny graphs of supersingular elliptic curves, showing optimal mixing times for random walks and applications to cryptography.

Delves into local degrees of continuous maps from the sphere, showcasing their role in calculating map degrees.

Explores the discrete log problem and index calculus method in cryptography.

Shows the equivalence between the index of a covering space's fundamental group and the degree of the covering space.