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Interlacing Families and Ramanujan Graphs
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Spectral Graph Theory: Introduction
Introduces Spectral Graph Theory, exploring eigenvalues and eigenvectors' role in graph properties.
Reformulating Problems: Tools and Intuition
Focuses on open problems and the importance of reformulating problems with better tools and intuition.
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.
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Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.
Isogenic Graphs: Spectral Analysis and Mathematical Applications
Explores isogenic graphs, spectral properties, and mathematical applications in modular forms and cryptography.
Pseudo Randomness in Graphs
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Covers graphical models for probabilistic distributions using graphs, nodes, and edges.
Unweighted Bipartite Matching
Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.
Stein Algorithm: Polynomial Identity Testing
Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.
Cheeger's Inequalities
Explores Cheeger's inequalities for random walks on graphs and their implications.