Applied Algebraic Topology Network Courses

On Characterizing Rare Events in Persistent Homology

Explore rare events in persistent homology, focusing on indecomposables in multi-parameter settings. Learn about large deviation principles and laws of large numbers in topological data analysis.

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

Farzana Nasrin - Random Persistence Diagram Generator

Explore a method for generating random persistence diagrams using parametric models and Markov chain Monte Carlo algorithms, with applications in material science and topology.

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

Robert Ghrist - Laplacians and Network Sheaves

Explore cellular sheaves, Laplacians, and network dynamics in algebraic topology. Learn about sheaf cohomology computation and applications in decentralized methods.

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

Vietoris-Rips Complexes of Hypercube Graphs

Explore Vietoris-Rips complexes of hypercube graphs, their collapsibility, and applications in genetic trees and persistent homology. Gain insights into simplicial complexes and topological data analysis.

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

Dejan Govc - Fundamental Groups of Small Simplicial Complexes

Explore minimal triangulations of manifolds and fundamental groups of small simplicial complexes, with insights on estimating vertex counts in minimal triangulations.

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

Efficient Invariant Embeddings for Universal Equivariant Learning

Explore efficient invariant embeddings for universal equivariant learning, focusing on group symmetries in machine learning tasks and their applications in various architectures like CNNs and graph neural networks.

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

Optimal Topological Simplification of Surfaces

Algorithmes et résultats de complexité pour simplifier la topologie des surfaces de manière optimale, en utilisant des courbes et graphes les plus courts possible.

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

Persistence Diagram Bundles- A Multidimensional Generalization of Vineyards

Explore persistence diagram bundles, a multidimensional generalization of vineyards for analyzing topological changes in data sets with multiple parameters, including computation methods and potential applications.

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

Analyzing Point Processes Using Topological Data Analysis

Explore point processes using topological data analysis, covering models, statistical techniques, and applications in spatial statistics. Learn to distinguish between process types and understand central limit theorems.

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

MD Simulations and Machine Learning to Quantify Interfacial Hydrophobicity

Explore molecular dynamics simulations and machine learning techniques to analyze interfacial hydrophobicity, focusing on efficient data analysis methods and topological approaches for complex chemical systems.

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

Yusu Wang - Graph Neural Network: Representational Power and Limitations

Explore graph neural networks' power and limitations, focusing on representation capabilities, Weisfeiler-Lehman tests, and universal approximation results for informed practical applications.

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

The Role of Solvent in Crystal Nucleation from Solution

Explore crystal nucleation mechanisms and solvent effects using advanced simulation methods. Gain insights into polymorph selection and solvent-dependent nucleation processes for various substances.

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

Topological Data Analysis of Plant-Pollinator Resource Complexes - Melinda Kleczynski

Explore topological data analysis in ecology, focusing on plant-pollinator interactions. Learn about resource complexes and insect-flower visitation patterns using advanced mathematical tools.

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

Vanessa Robins - The Extended Persistent Homology Transform for Manifolds with Boundary

Explore extended persistent homology transform for shape analysis, offering finite distances between shapes with different Betti numbers and applications in shape clustering.

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

Chromatic Number of G-Borsuk Graphs

Explore G-Borsuk graphs, their chromatic numbers, and topological connections. Delve into G-actions, Hom-complexes, and random graph thresholds for a deeper understanding of this algebraic topology concept.

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