Applied Algebraic Topology Network Courses

Graph Representation Learning and Its Applications to Biomedicine

Graph representation learning techniques for biomedical applications, focusing on SubGNN for disentangled subgraph embeddings and their use in predicting disease treatments and safe drug combinations.

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

Liquid Crystals Dynamics - What Persistent Homology Reveals

Explore liquid crystal phase transitions through persistent homology, revealing thermodynamic features and structural changes in nanocomposites using advanced data analysis techniques.

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

Topological Complexity of Pure Graph Braid Groups

Explore topological complexity in graph braid groups, focusing on Farber's conjecture about ordered configuration spaces and its implications for topological robotics.

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

Nonlinear Dynamics in an Age of Heuristic Science

Explore nonlinear dynamics through combinatorial topology, offering efficient computational methods and new perspectives for multiscale systems and data-driven science in biology and engineering.

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

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