Realisation of Cycles and Small Covers Over Graph Associahedra
Explore graph associahedra, focusing on realisation of cycles and small covers. Gain insights into this advanced mathematical topic through expert analysis and explanations.
Jacobians of Circulant Graphs
Explore Jacobians of circulant graphs with A. D. Mednykh, delving into advanced mathematical concepts and their applications in graph theory and topology.
Colored Graphs and Complements of Knots and Links
Explore 4-colored graphs and their relationship to knot and link complements, delving into topological concepts and graph theory applications in knot theory.
Branched Coverings and Harmonic Automorphisms of Graphs
Explore branched coverings and harmonic automorphisms of graphs with Alexander Mednykh, delving into advanced mathematical concepts and their applications in quantum topology.
Matroids, Delta Matroids, and Knot Invariants
Explore matroids, delta matroids, and their applications in knot theory with Sergei Lando. Gain insights into these mathematical structures and their role in understanding knot invariants.
Discrete Mathematics
Explore logic, probability, graph theory, relations, and combinatorics in this comprehensive mathematics course, enhancing problem-solving skills and mathematical reasoning abilities.
Generational Random Graphs – Professor Jon Crowcroft
Explore generational random graphs and their applications in network analysis, focusing on small-world-like graphs and heterogeneous models. Learn from expert Jon Crowcroft's insights and theories.
Factorization-based Sparse Solvers and Preconditioners - Lecture 3
Explore factorization-based sparse solvers and preconditioners, covering topics like minimum degree ordering, numerical pivoting, and sparse Gaussian elimination techniques.
Applications in Extremal Combinatorics - Lecture 2
Explore advanced concepts in extremal combinatorics, focusing on analytical techniques and their applications in theoretical computer science.
Applications in Extremal Combinatorics - Lecture 1
Explore advanced concepts in extremal combinatorics, focusing on analytical techniques and their applications in theoretical computer science.
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 Alignment: Informational and Computational Limits - Lecture 2
Explore graph alignment challenges, focusing on informational and computational limits. Gain insights into probabilistic and optimization methods for data science applications.
Alignment of Random Graphs: Informational and Computational Limits - Lecture 2
Explores informational and computational limits in aligning random graphs, focusing on advanced probabilistic techniques for data science and graph theory applications.
Alignment of Random Graphs: Informational and Computational Limits - Lecture 1
Explore informational and computational limits of random graph alignment in this lecture by Laurent Massoulié, part of a data science discussion on probabilistic and optimization methods.
Small-Set Expansion in the 2-Degree Short-Code Graph - The Easier Version
Explore the intricacies of small-set expansion in the 2-degree short-code graph, focusing on an easier version of this complex mathematical concept.
On Perfectly Friendly Bisections of Random Graphs
Explores vertex-isoperimetry expansion in random graphs, using boolean function tools to prove equipartition results with specific neighbor distribution properties across partitions.
Reverse Hypercontractivity and Improved Sampling in High Dimensional Expanders
Explore reverse hypercontractivity in high-dimensional expanders, its connection to mixing and sampling, and discover new Chernoff-like bounds in these mathematical structures.
Higher-Dimensional Expansion of Random Geometric Complexes
Explores 2-dimensional spectral expansion in hypergraphs, demonstrating that triangles in high-dimensional random geometric graphs form expanding simplicial complexes of low polynomial degree.
Testing Thresholds for High-Dimensional Sparse Random Geometric Graphs
Explores distinguishing Erdős-Rényi from random geometric graphs, improving bounds on statistical indistinguishability thresholds using Belief Propagation and sphere geometry analysis.