Computational Topology Courses and Certifications

Institut Henri Poincaré

Two-Dimensional Computational Topology

Explore two-dimensional computational topology through algorithmic approaches to geometric problems in this comprehensive lecture series by Jeff Erickson.

• YouTube
• 6 hours 30 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Javier Arsuaga - Applications of Computational Topology to the Analysis of Breast Cancer

Explore computational topology's role in breast cancer analysis, uncovering new insights through advanced mathematical techniques and data visualization methods.

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

SAIConference

Understanding Complex Biological Systems: A Journey into Computational Topology

Explore computational topology's role in decoding complex biological systems. Learn how algorithms interpret data from molecular biology, genetics, and medicine, offering unique insights into disease progression and protein structures.

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

Applied Algebraic Topology Network

Scalable Computation of the Extremum Graph

Explore scalable computation of extremum graphs, a simplified topological descriptor for scalar functions, with applications in visualization and shape analysis. Learn efficient parallel algorithms for large datasets.

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

Applied Algebraic Topology Network

Embeddings and Tverberg-Type Problems: New Algorithms and Undecidability Results

Explore computational topology: algorithmic embeddability, undecidability in higher dimensions, and polynomial-time decidability of r-Tverberg problem in metastable range.

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

Applied Algebraic Topology Network

Every Stable Invariant of Finite Metric Spaces Produces False Positives

Explore stable invariants in computational topology, their limitations in approximating Gromov-Hausdorff distance, and the inevitability of false positives when using Hilbert space-valued invariants.

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

Applied Algebraic Topology Network

Wasserstein Distances, Geodesics and Barycenters of Merge Trees

Explore computational frameworks for merge trees, including Wasserstein distances, geodesics, and barycenters. Learn efficient algorithms and applications in visualization, feature tracking, and ensemble clustering.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Multiscale Many-body Correlations and Structure in Chemistry Data

Integrating graphs, topology, and geometry to analyze complex chemistry data, providing insights into multiscale correlations and structures beyond traditional methods.

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

Applied Algebraic Topology Network

Persistence-Based Skeletonization of Images

Explores algorithms for splitting images into convex polygons using topological persistence, including Convex Constrained Mesh and Persistent Resolution-Independent Mesh for edge detection.

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

Applied Algebraic Topology Network

Pawel Dlotko - A Few Simple Stories on Topology in Action

Explore practical applications of computational topology in material science, dynamical systems, and brain research. Learn how theory and algorithms work together to solve real-world problems.

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

Applied Algebraic Topology Network

Bradley Nelson: Parameterized Vietoris-Rips Filtrations via Covers

Explore computational topology techniques for large filtered geometric complexes, focusing on Vietoris-Rips filtrations and cover-based methods for parallel computation and compression.

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

Applied Algebraic Topology Network

Demystifying Latschev's Theorem for Manifold Reconstruction

Explores quantitative approaches to Latschev's theorem for topological manifold reconstruction, advancing finite sample analysis in data science and manifold learning applications.

• YouTube
• 49 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

Hausdorff Center for Mathematics

Applied and Computational Algebraic Topology

Explore advanced applications of algebraic topology in neural networks, distributed computing, persistence homology, and geometric analysis through expert lectures.

• YouTube
• 22 hours 9 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Applied Algebraic Topology Methods, Computation, and Science - ATMCS/AATRN 2020

Explore cutting-edge research in applied algebraic topology through expert presentations on persistence diagrams, homology, and computational methods for data analysis.

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