Applied Algebraic Topology Network Courses

A Topological Study of the Space of Planar Pentagons

Exploring topology of planar pentagons as a model for molecular conformation spaces, using topological data analysis for dimensionality reduction and visualization.

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

Exchanging Replicas with Unequal Cost, Infinitely and Permanently

Innovative replica exchange method for parallel simulations with varying computational costs, enhancing efficiency in Monte Carlo algorithms and path sampling techniques.

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

A Topological Understanding of Neuronal Morphologies

Exploring topological data analysis for neuronal morphologies, from single cells to networks. Highlights applications in classification, clustering, and solving inverse problems in neuroscience.

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

Dmitri Burago: A Mozaic from Geometry, Dynamics, PDEs, and Maybe More

Explore unsolved problems and recent progress in geometry, dynamics, and PDEs through a mosaic of interconnected topics, featuring insights from collaborative research.

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

Saecular Persistence

Explore saecular persistence, a method to decompose persistence modules with non-field coefficients. Learn about applications in topology, generalized persistence diagrams, and scientific data analysis.

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

Homotopy Coherence - Theme and Variations

Explore homotopy coherence theory's evolution, applications, and links to representation theory in this semi-historical survey, offering unique insights and connections in algebraic topology.

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

Alexander Dranishnikov - On the LS-Category of Group Homomorphisms

Exploration of LS-category equality for group homomorphisms, discussing proofs for specific group classes and presenting a counterexample for geometrically finite groups.

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

Persistent Cycle Registration and Topological Bootstrap

Novel approach for comparing persistent homology representations, utilizing spatial placement of persistent cycles. Demonstrates application in topological inference to differentiate signal from noise in point cloud data.

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

Frédéric Chazal Interviewed by Steve Oudot

Entretien approfondi avec Frédéric Chazal, pionnier de la topologie appliquée, explorant son parcours, ses contributions majeures et sa vision pour l'avenir du domaine.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

On the Weak Topological Complexity and the TC-Ganea Conjecture

Explores weak topological complexity and TC-Ganea conjecture, discussing conditions for spaces to satisfy TC(X x S^n)=TC(X)+TC(S^n) and presenting counterexamples to the conjecture.

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

Henry Adams - Topology in Machine Learning

Explore persistent homology in machine learning, covering applications in materials science, computer vision, and agent-based modeling. Learn how topology relates to dataset geometry and explainable AI.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Homology Inference for the Degree-Rips Bifiltration

Explore density-sensitive degree-Rips bifiltration, its homology inference framework, and applications to annular point clouds with outliers. Analyze homotopy types and explanatory power in topological data analysis.

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

Swap, Shift and Trim to Edge Collapse a Flag Filtration

Exploring efficient algorithms for reducing flag filtrations in persistent homology, with focus on edge collapse techniques and their applications in computational topology.

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

The Topological Complexity of Pure Graph Braid Groups Is Stably Maximal

Explore the topological complexity of configuration spaces in graphs, using group theoretic estimates for higher topological complexity instead of traditional cohomology approaches.

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

Computation of Reeb Graphs in a Semi-Algebraic Setting

Explore semi-algebraic geometry in applied topology, focusing on Reeb graphs and spaces. Learn about an efficient algorithm for computing semi-algebraic descriptions of Reeb graphs.

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