Topology Courses and Certifications

Applied Algebraic Topology Network

Persistent Homotopy Groups of Metric Spaces

Exploring persistent homotopy groups of metric spaces, blending topology and geometry to capture dataset features beyond persistent homology, with applications and stability properties.

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

Applied Algebraic Topology Network

Yevgeny Liokumovich - Urysohn Width, Isoperimetric Inequalities and Scalar Curvature

Explore metric spaces, Hausdorff measure, and continuous mappings. Discover connections to isoperimetric inequalities and Riemannian geometry's positive scalar curvature.

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

Applied Algebraic Topology Network

Geometry and Topology of Decision

Explore geometric and topological approaches to decision-making when faced with conflicting expert opinions, examining theoretical concepts and practical applications in various scenarios.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Kathryn Hess - Bedlewo: Topology Meets Neuroscience

Explore how topology applies to neuroscience across scales, from neurons to brain regions. Discover topological analysis of microconnectomes and neuron classification, with insights into brain imaging data.

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

Applied Algebraic Topology Network

Peter Bubenik - Statistical Topological Data Analysis

Explore statistical methods for analyzing topological data, combining mathematical concepts with practical applications in data science and machine learning.

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

Applied Algebraic Topology Network

Topology and Combinatorics of Fair Division

Explore the intersection of topology and combinatorics in fair division problems, examining mathematical techniques for equitable resource allocation and distribution.

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

International Mathematical Union

Sausages and Butcher Paper

Explore geometric principles through everyday objects, unraveling complex mathematical concepts with accessible examples and innovative visualizations.

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

Applied Algebraic Topology Network

Topology of Artificial Neuron Activations in Deep Learning

Explore the topology of artificial neuron activations in deep learning, from image classification to natural language processing, with insights on convolutional neural networks and transformer-based models.

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

Hausdorff Center for Mathematics

P-adic Geometry - Topologies, Diamonds and the Fargues-Fontaine Curve

Explore advanced p-adic geometry concepts, including topologies, diamonds, and the Fargues-Fontaine curve in this in-depth mathematical lecture.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 13

Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.

• YouTube
• 1 hour 33 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 20

Explore advanced concepts in topology, including complex mathematical structures and their properties, in this comprehensive lecture by Bruno Zimmerman.

• YouTube
• 1 hour 38 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 10

Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 4

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

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 6

Explore fundamental concepts and advanced techniques in topological spaces, including continuity, compactness, and connectedness, with expert guidance from Bruno Zimmerman.

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

ICTP Mathematics

Topology - Lecture 2

Explore fundamental concepts of topology, including topological spaces, continuity, and homeomorphisms, with a focus on mathematical rigor and abstract reasoning.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video