Lectures related to Spectral graph theory

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.

Isogenic Graphs: Spectral Analysis and Mathematical Applications

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

Consensus Algorithms: Weight Assignment and Applications

Explores the design of graph weights for consensus and applications in sensor networks.

Pseudorandomness: Theory and Applications

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

Ramanujan Graphs: Generating Functions and Expander Graphs

Explores Ramanujan graphs, generating functions, non-backtracking walks, and expander graphs in relation to NP-hard problems.

Interlacing Families and Ramanujan Graphs

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

Distributed Computation: Consensus Algorithms in Networked Control Systems

Explores consensus algorithms in networked control systems, covering topics like Metropolis-Hasting models and distributed computation of Least-Squares regression.

Bipartite Graphs: Independent Sets

Explores bipartite graphs, independent sets, Shearer's Lemma, labeled graphs, and entropy analysis.

Sparsest Cut and Concurrent Flow

Covers sparsest cut, NP-completeness, Bougains Theorem, and concurrent flow in graphs.

Cheeger's Inequalities

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

Algebraic Graph Theory: Matrices and Connectivity

Explores algebraic graph theory applied to networked control systems and consensus algorithms.

Networked Control Systems: Laplacian Flow and Heat Equation

Explores Laplacian flow, heat equation analogies, and microgrid networked controllers.

Graph Models and Brain Connectomics

Explores graph theory in brain connectomics, MRI applications, network analysis relevance, and individual fingerprinting.

Spectral Graph Theory: Introduction

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

Graphs and Phase: Understanding Amplitude and Phase Relationships

Analyzes amplitude and phase graphs, emphasizing force concentration and phase shift.

Pseudorandomness: Expander Mixing Lemma

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

Graph Theory Fundamentals

Explores fundamental graph theory concepts, Erdős' results, Chromatic Lemma, and Union Bound theorem in graph theory.

Cheeger's Inequality

Explores Cheeger's inequality and its implications in graph theory.

Non-parametric regression for networks

Explores non-parametric regression for networks, covering object data analysis, network graphs, extrinsic distances, and practical projections.

Networked Control Systems: Laplacian Matrix and Consensus

Explores the Laplacian matrix and consensus in networked control systems.