Sparsest Cut: (log n) Approximation Algorithm

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Equidistribution of CM Points

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Intermediate Values Theorem

Explores the Intermediate Values Theorem for continuous functions on closed intervals.

Approximation Algorithms

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Green's Theorem in 2D: Applications

Explores the applications of Green's Theorem in 2D, emphasizing the importance of regular domains for successful integration.

Implicit Functions Theorem

Covers the Implicit Functions Theorem and its applications in finding extremums under constraints.

Cauchy-Lipschitz Theorem

Explores the Cauchy-Lipschitz theorem for differential equations and its proof.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Stokes Theorem

Covers the Stokes theorem, extending the Green theorem to surfaces in R3 and explaining its application.

Closed Curves and Topological Spaces

Explores closed curves in topological spaces, emphasizing their properties and significance in mathematics.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.