Lecture

Sparsest Cut: (log n) Approximation Algorithm

Related lectures (29)

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Geodesic Convexity: Theory and Applications

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Algorithms & Growth of Functions

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Curve Integrals: Gauss/Green Theorem

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Analysis I: Indeterminate Forms and Gendarmes' Role

Covers indeterminate forms, logarithmic functions, and the 'role of the gendarmes' theorem.

Cauchy Equations and Integral Decomposition

Covers the application of Cauchy equations and integral decomposition, addressing questions related to holomorphic functions and Jacobian matrices.

Concept of Proof in Mathematics

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

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.