Isogenic Graphs: Spectral Analysis and Mathematical Applications

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Related lectures (30)

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Building Ramanujan Graphs

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

Interlacing Families and Ramanujan Graphs

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

Isogeny Graphs: Eigenvalues and Cryptography

Explores isogeny graphs of supersingular elliptic curves, showing optimal mixing times for random walks and applications to cryptography.

Spectral Clustering: Theory and Applications

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

Graphs: BFS

Introduces elementary graph algorithms, focusing on Breadth-First Search and Depth-First Search.

Graphical Models: Probability Distributions and Factor Graphs

Covers graphical models for probability distributions and factor graphs representation.

Cheeger's Inequality

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

Matrix Tree Theorem

Explores the Matrix Tree Theorem and its application in calculating spanning trees in graphs.

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.

Networked Control Systems: Properties of Laplacian Matrices

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