Simplicial Complexes Courses and Certifications

Fields Institute

Flag Complexes, Polyhedral Products and Geometric Group Theory

Explore connections between flag complexes, polyhedral products, and geometric group theory in this advanced mathematics lecture by Stephen Theriault from the University of Southampton.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Fields Institute

Properties of Polyhedral Products

Explore properties of polyhedral products in this advanced mathematics lecture, covering key concepts and applications in toric topology and geometry.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Fields Institute

The Davis-Januszkiewicz Construction Reinterpreted and Generalized

Explore a reinterpretation and generalization of the Davis-Januszkiewicz construction in toric topology, presented by Anthony Bahri from Rider University as part of the Graduate School on Toric Topology.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

Fields Institute

An Introduction to Polyhedral Products

Explore the foundations of polyhedral products in this graduate-level lecture, covering key concepts and applications in toric topology and geometry.

• YouTube
• 1 hour 6 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

IMSA

Anisotropy, Biased Pairings and the Lefschetz Property - January 30, 2024

Explore anisotropy in face rings of simplicial spheres, biased pairing property, and Hall-Laman relations. Discover their connections to the Lefschetz property in advanced mathematics.

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

Institute for Pure & Applied Mathematics (IPAM)

Classical Topology and Quantum Complexity - IPAM at UCLA

Explore the intersection of classical topology and quantum complexity, focusing on computational challenges in determining homology groups and their implications for quantum mechanics and data analysis.

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

Stony Brook Mathematics

The High-Degree Rational Cohomology of the Special Linear Group

Explore high-degree rational cohomology of SL_n(Z) and SL_n(R) for number rings. Examine Steinberg modules and associated simplicial complexes to understand special linear group cohomology.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Waists Measured via Urysohn Width in Riemannian Manifolds

Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

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.

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

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

Institute for Advanced Study

The Schubert Variety of a Pair of Linear Spaces

Delve into advanced mathematical concepts exploring Schubert varieties, Kempf collapsing, and matroid theory through the lens of linear spaces and their geometric relationships.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Interactions and Topological Synchronization in Simplicial Kuramoto Model

Delve into the mathematical foundations of simplicial Kuramoto models, exploring oscillator dynamics, topology-geometry relationships, and synchronization patterns in complex networks.

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

Applied Algebraic Topology Network

Persistent Homology of Plant-Pollinator Interactions - The Importance of Flowering Plant Surveys

Explore persistent homology in plant-pollinator interactions, analyzing topological features and the impact of flowering plant surveys on understanding community structures.

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