Pseudorandomness: Theory and Applications

Related lectures (29)

Page 3 of 3

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

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

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

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

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

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Explores automorphisms of graphs, focusing on automorphism groups, Cayley-Abels graphs, and quasi-isometry.

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

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.