Lecture

Pseudorandomness: Theory and Applications

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

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

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

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

Explores the role of graphs in deep learning, focusing on their structure, applications, and techniques for processing graph data.

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

Explores pseudo randomness in graphs using eigenvalues and polynomials, emphasizing the significance of bunched roots and common interlacers.

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

Covers graph properties, representations, and traversal algorithms using BFS and DFS.

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

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

Introduces the basics of graphs and networks, covering definitions, paths, trees, flows, circulation, and spanning trees.

Explores graphs and matrices, including adjacency, degree, and Laplace matrices, Matrix-tree theorem, and spanning trees.

Covers handling network data, types of graphs, centrality measures, and properties of real-world networks.

Explores automorphism groups in trees and graphs, focusing on ends and types of automorphisms.

Covers matrices, linear applications, vector spaces, and bijective functions.

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

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Delves into optimization on manifolds, showcasing simple applications like finding largest eigenvalues and singular values.

Explores the connection between graphs and probabilities, emphasizing modular and super modular probabilities and correlation properties.