Lectures related to Building Ramanujan Graphs

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

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

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

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

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

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

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Explores the application of matrices and eigendecompositions in networks.

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

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

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

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.

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

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

Explores the diagonalization of matrices and the conditions for exact diagonalization, with examples demonstrating the process.

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

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

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