Lectures related to Expander Graphs: Properties and Eigenvalues

Interlacing Families and Ramanujan Graphs

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

Interlacing Families and Ramanujan Graphs

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

Pseudorandomness: Expander Mixing Lemma

Explores pseudorandomness and the Expander Mixing Lemma in the context of d-regular graphs.

Building Ramanujan Graphs

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

Pseudorandomness: Theory and Applications

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Graph Theory and Network Flows

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

Statistical Analysis of Network Data

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.

Spectral Graph Theory: Introduction

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

Graphs: Properties and Representations

Covers graph properties, representations, and traversal algorithms using BFS and DFS.

Graphical Models: Probability Distributions and Factor Graphs

Covers graphical models for probability distributions and factor graphs representation.

Reformulating Problems: Tools and Intuition

Focuses on open problems and the importance of reformulating problems with better tools and intuition.

Isogenic Graphs: Spectral Analysis and Mathematical Applications

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

Graph Algorithms: Modeling and Traversal

Covers graph algorithms, modeling relationships between objects, and traversal techniques like BFS and DFS.

Szemerédi Regularity Lemma

Explores the Szemerédi Regularity Lemma, e-regularity in bipartite graphs, supergraph structure, and induction techniques.

Minimum Spanning Trees: Prim's Algorithm

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

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.

Spectral Clustering: Theory and Applications

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

Graph Algorithms: Modeling and Representation

Covers the basics of graph algorithms, focusing on modeling and representation of graphs in memory.

Networked Control Systems: Properties and Connectivity

Explores properties of matrices, irreducibility, and graph connectivity in networked control systems.