Simplicial Complexes Courses and Certifications

ICTP Condensed Matter and Statistical Physics

Topology and Dynamics of Higher-Order Networks - Lecture 1: General Introduction to Algebraic Topology on Networks and Simplicial Complexes

Explore algebraic topology in networks and simplicial complexes, focusing on homology and boundary operators. Gain insights into higher-order network structures and their impact on complex systems.

• YouTube
• 2 hours 16 minutes
• On-Demand
• Free Video

ICTP Condensed Matter and Statistical Physics

Topology and Dynamics of Higher-Order Networks - Lecture 2: Introduction to Algebraic Topology on Networks and Simplicial Complexes

Explore algebraic topology on networks and simplicial complexes, focusing on Hodge Laplacians and Dirac operators in higher-order networks. Gain insights into topological signals and their applications.

• YouTube
• 2 hours
• On-Demand
• Free Video

Applied Algebraic Topology Network

Tools for Homotopy Computations in Simplicial Complexes from Graphs

Explore computational methods for determining homotopy types in independence complexes, with applications to clique and matching complexes in graph theory.

• YouTube
• 10 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Vertex Order Shellings in Simplicial Complexes

Delve into the mathematical exploration of vertex order shellings in simplicial complexes, examining their topological properties and relationship with matroid independence complexes through Björner's theorem.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Fields Institute

Topological Complexity of Random Simplicial Complexes

Explore topological complexity in random simplicial complexes through advanced mathematical analysis and computational methods.

• YouTube
• 55 minutes
• On-Demand
• Free Video

IMSA

Simplicial Complexes and Face Rings - January 29, 2024

Explore simplicial complexes and face rings, including stars and links, and their correspondence in Stanley-Reisner rings. Gain insights into fundamental concepts of algebraic topology.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

High Connectivity of Random Simplicial Complexes and Their Topological Complexity

Explore combinatorial tools for analyzing homotopical connectivity in random simplicial complexes and their asymptotic topological properties.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

A Limit Theorem for Betti Numbers of Random Simplicial Complexes

Explore asymptotic behavior of Betti numbers in homogeneous and spatially independent random simplicial complexes, extending previous work on Linial-Meshulam complexes using local weak convergence.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

From Large to Infinite Random Simplicial Complexes

Explore two models of random simplicial complexes extending the Erdos-Renyi model, examining their Alexander duality relation and the unique infinite Rado simplicial complex.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Omer Bobrowski - Random Simplicial Complexes

Explore higher-dimensional generalizations of random graphs, focusing on random d-complexes and Cech complexes. Learn about connectivity, cycle formation, and giant components in these structures.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Omer Bobrowski - Random Simplicial Complexes, Lecture I

Explore random simplicial complexes, their applications in data analysis, and key phenomena like connectivity and cycle formation. Includes introduction to algebraic topology and homology theory.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Introduction to Algebraic Topology

Explore algebraic invariants of topological spaces through fundamental groups, homology groups, and covering spaces with computational techniques and mathematical applications.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Centre International de Rencontres Mathématiques

Random Walks on Simplicial Complexes

Explore random walks on simplicial complexes in this mathematical conference talk, delving into advanced concepts and applications in the field.

• YouTube
• 55 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 3

Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video

Insights into Mathematics

Delta Complexes, Betti Numbers, and Torsion in Algebraic Topology

Explore homology groups of torus and projective plane using delta-complexes. Learn about Betti numbers and torsion in algebraic topology, with practical computations and insights into fundamental concepts.

• YouTube
• 48 minutes
• On-Demand
• Free Video