Spectral Aspects of Symmetric Matrix Signings
Explore symmetric matrix signings, their spectral aspects, and applications in graph theory, polynomial identity testing, and algorithmic problems.
Spectral Graph Theory - Eigenvalues at CMU - Lecture 15a of CS Theory Toolkit
Explore eigenvalues of the Laplacian and Markov operator in spectral graph theory, including associated formulas and their applications in theoretical computer science research.
Spectral Graph Theory - Minimizing/Maximizing the Quadratic Form
Explore spectral graph theory, focusing on minimizing and maximizing quadratic forms, with connections to graph components and bipartiteness in this graduate-level lecture.
Spectral Graph Theory - The Quadratic Form
Explores spectral graph theory, focusing on the quadratic form associated with undirected graphs. Covers basic setup and provides examples for graduate-level computer science research.
Spectral Graph Theory - Lecture 1
Explore spectral graph theory, covering self-adjoint matrices, Rayleigh equalities, graph isomorphism, Cayley graphs, and automorphism groups. Gain insights into complex systems and network analysis.
High-Dimensional Expanders - Lecture 1
Explore high-dimensional expanders with Irit Dinur, delving into advanced concepts in analysis and theoretical computer science.
High-Dimensional Expanders - Lecture 4
Explore advanced concepts in high-dimensional expanders, focusing on analysis techniques and applications in theoretical computer science.
High-Dimensional Expanders - Lecture 3
Explore advanced concepts in high-dimensional expanders, focusing on analysis techniques and applications in theoretical computer science.
Graph Linear Algebra Part 1
Explore fundamental concepts of graph linear algebra, focusing on matrices, spectral theory, and their applications in algorithmic graph theory and network analysis.
Graph Linear Algebra Part 3 - Data Structures and Optimization for Fast Algorithms
Explore advanced graph linear algebra concepts and optimization techniques for fast algorithms in data structures, building on previous parts.
Graph Linear Algebra Part 2
Explore advanced concepts in graph linear algebra, focusing on data structures and optimization techniques for developing efficient algorithms.
A New Approach to Strong Convergence - Lecture 1
Explore a novel approach to strong convergence in graph theory, addressing Alon's conjecture and extending Friedman's theorem with applications to random graphs, geometry, and operator algebras.
Expanders and Property Testing
Explore expanders and property testing in graph theory, focusing on their applications and connections to theoretical computer science.
Perturbation of Fiedler Vector: Interest for Graph Measures and Shape Analysis
Explore Fiedler vector perturbation and its applications in graph measures and shape analysis, gaining insights into advanced mathematical concepts.
Multiscale Basis Dictionaries and Scattering Networks on Simplicial Complexes
Explore multiscale basis dictionaries and scattering networks on simplicial complexes, focusing on HGLET and GHWT. Learn applications in coauthorship/citation complex and article classification.
Online Algorithms for Spectral Hypergraph Sparsification
Explore online algorithms for spectral hypergraph sparsification, focusing on space-efficient methods for handling streaming hyperedges and producing accurate sparsifiers.
Interlacing Families and Ramanujan Graphs - #ICBS2024
Explore Ramanujan Graphs, interlacing families, and their connections to various mathematical fields. Gain insights into recent developments and open problems in graph theory.
Exponentially Many Graphs Are Determined by Their Spectrum
Explore discrete analogues of Kac's question on "hearing the shape of a drum" and learn about graphs determined by their spectrum in this mathematical seminar.
Analytic and Reidemeister Torsions of Digraphs and Path Complexes
Explore Reidemeister and analytic torsions on finite digraphs using path homology theory. Learn about Hodge Laplace operators, torsion identities, and formulas for Cartesian products and joins.
Equiangular Lines and Eigenvalue Multiplicity - ICBS 2024
Explore equiangular lines in high dimensions, solving a longstanding problem using spectral graph theory and discussing future research directions.
Local Hamiltonians and Quantum Cuts: Exploring the Quantum Heisenberg Model
Delve into quantum Heisenberg models and their connection to Max-Cut problems, exploring theoretical frameworks and approximation algorithms for Quantum Max-d-Cut Hamiltonians in computational physics.