Applied Algebraic Topology Network Courses

Luis Scoccola - Locally Persistent Categories & Metric Properties of Interleaving Distances

Explore locally persistent categories, metric properties of interleaving distances, and their applications in algebraic topology, including natural interleavings and weak equivalences.

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

Computing Gromov-Hausdorff Distances Between Ultrametric Spaces

Explore efficient algorithms for computing Gromov-Hausdorff distances between ultrametric spaces, including complexity analysis and dynamic programming approaches.

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

Ling Zhou - Persistent Homotopy Groups of Metric Spaces

Explore persistent homotopy groups of metric spaces, covering discrete fundamental groups, stability theorems, and persistent rational homotopy in this advanced topology lecture.

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

Nathanael Cox - Effective Algorithms for Quotients of Semi-Algebraic Equivalence Relations

Explore efficient algorithms for computing quotients of semi-algebraic equivalence relations, focusing on complexity, tools, and key results in applied algebraic topology.

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

Tomoo Yokoyama - Generalizations of Morse Graph of Flows and Reeb Graph of Hamiltonian Flows

Generalizations of Morse and Reeb graphs for flows, exploring connections between dynamical systems, topological structures, and abstract orbit spaces. Insights into Conley theory and topological invariants.

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

Takashi Owada - Limit Theorems for Topological Invariants of the Dynamic Multi-Parameter Simplicial Complex

Explore topological invariants in dynamic multi-parameter simplicial complexes, covering connectivity, probability, and limiting processes in applied algebraic topology.

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

An Upper Bound on the Topological Complexity of Discriminantal Varieties

Explore upper bounds on topological complexity of discriminantal varieties, with applications to configuration spaces. Combines Morse theory, equivariant homotopy theory, and complex geometry.

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

Vanessa Robins Interviewed by Elizabeth Bradley

Explore applied topology with Vanessa Robins as she discusses her career journey, research interests, and insights on granular materials, collaborations, and emerging areas in the field.

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

Cuneyt Akçora - TDA on Networks – Applications and Scalability Issues

Explore Topological Data Analysis on networks, focusing on applications in blockchain for ransomware detection, price prediction, and anomaly detection. Learn about persistent homology and TDAMapper algorithms.

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

Bala Krishnamoorthy - Steinhaus Filtration and Stable Paths in the Mapper

Explore Steinhaus filtration and stable paths in Mapper, a topological data analysis tool. Learn applications in recommendation systems and explainable machine learning for data-driven insights.

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

Sampling Smooth Manifolds Using Ellipsoids

Explore sampling smooth manifolds using ellipsoids, a novel approach requiring lower sample density than traditional ball-based methods, with potential applications in data science and topology.

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

Henry Adams - Fair Division

Explore how Sperner's lemma and topology can solve fair rent division among roommates with differing preferences, based on research and a New York Times article.

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

Moduli Spaces of Morse Functions for Persistence

Exploring Morse functions on surfaces, focusing on decomposition, elementary moves, and embeddings. Insights into persistence barcodes and the inverse problem through nesting posets of level sets.

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

Topological Simplification of Voxelized Data

Explore topological simplification of voxelized data, focusing on homological methods to enhance graphical data analysis in scientific fields like medicine and biology.

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

Exploring Brain Dynamics During Ongoing Cognition Using Mapper

Exploring brain dynamics using Mapper: analyzing fMRI data with geometric techniques to reveal whole-brain activity patterns and predict task performance in multitask paradigms.

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