Applied Algebraic Topology Network Courses

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

Detecting Bifurcations in Dynamical Systems with Zigzag Persistent Homology

Explore zigzag persistent homology for efficient detection of bifurcations in dynamical systems, reducing computational costs and capturing topological changes in a single persistence diagram.

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

Alexander Wagner - Nonembeddability of Persistence Diagrams into Hilbert Spaces

Explore nonembeddability of persistence diagrams in Hilbert spaces, examining stability, metrics, and implications for machine learning applications in topological data analysis.

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

Computing Persistent Homology - Introduction

Explore the fundamentals of persistent homology computation, covering key concepts, intuition, and practical applications in topological data analysis.

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

Geometric and Topological Data Analysis of Enzyme Kinetics

Explore geometric and topological data analysis techniques applied to enzyme kinetics, focusing on ERK molecular dynamics and its implications for cancer and developmental defects.

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

Statistical Invariance of Betti Numbers in the Thermodynamic Regime

Explore statistical invariance of Betti numbers in random topology, examining conditions for topological inference through parametric statistics lens. Investigates asymptotic behavior and group invariance concepts.

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

Hardness Results in Discrete Morse Theory for 2-Complexes

Explore inapproximability and parameterized complexity in discrete Morse theory for 2-complexes, focusing on minimizing critical simplices and presenting new hardness results and an approximation algorithm.

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

Hengrui Luo - Generalized Penalty for Circular Coordinate Representation

Explore dimension reduction using circular coordinates and generalized penalties in topological data analysis. Enhance visualization of high-dimensional datasets while preserving topological structures.

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

Generalized Persistence Algorithm for Decomposing Multi-Parameter Persistence Modules

Explore a generalized persistence algorithm for decomposing multi-parameter persistence modules, enhancing topological data analysis with improved computational efficiency and structural insights.

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

Conley-Morse-Forman Theory for Generalized Combinatorial Multivector Fields

Generalized combinatorial multivector fields on finite topological spaces: extending Conley-Morse-Forman theory for data science applications, including isolated invariant sets, Conley index, and Morse decompositions.

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

A Canonical Framework for Summarizing Persistence Diagrams

Explore a canonical framework for summarizing persistence diagrams in topological data analysis, including theoretical foundations, applications, and future developments.

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

A Limit Theorem for Betti Numbers of Random Simplicial Complexes

Explore asymptotic behavior of Betti numbers in homogeneous and spatially independent random simplicial complexes, extending previous work on Linial-Meshulam complexes using local weak convergence.

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