Lecture

Cheeger's Inequality

Related lectures (29)

Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.

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.

Spectral Graph Theory: Introduction

Introduces Spectral Graph Theory, exploring eigenvalues and eigenvectors' role in graph properties.

Cheeger's Inequalities

Explores Cheeger's inequalities for random walks on graphs and their implications.

Sparsest Cut: Leighton-Rao Algorithm

Covers the Leighton-Rao algorithm for finding the sparsest cut in a graph, focusing on its steps and theoretical foundations.

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Interlacing Families and Ramanujan Graphs

Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.

Graph Sketching: Connected Components

Covers the concept of graph sketching with a focus on connected components.

Cheeger's Inequalities

Covers Cheeger's inequalities and the combinatorial properties of graphs.

Spectral Clustering: Theory and Applications

Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.

Sparsest Cut: Bourgain's Theorem

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Isogenic Graphs: Spectral Analysis and Mathematical Applications

Explores isogenic graphs, spectral properties, and mathematical applications in modular forms and cryptography.

Interlacing Families and Ramanujan Graphs

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Matrices and Networks

Explores the application of matrices and eigendecompositions in networks.

Matroids: Matroid Intersection

Covers the concept of matroids, focusing on matroid intersection and the properties of subsets of a ground set.

Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

Discusses the Ford-Fulkerson method and strongly connected components in graph algorithms.

Expander Graphs: Properties and Eigenvalues

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Graph Theory and Network Flows

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

Building Ramanujan Graphs

Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.

Networked Control Systems: Properties of Laplacian Matrices

Explores Laplacian matrix properties in networked control systems and their relation to graph theory.