Persistence Modules Courses and Certifications

Applied Algebraic Topology Network

Parallel Decomposition of Persistence Modules Through Interval Bases

Exploring parallel decomposition of persistence modules using interval bases, with applications in Topological Data Analysis and connections to the Hodge Laplacian.

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

Applied Algebraic Topology Network

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

Applied Algebraic Topology Network

Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules

Efficient algorithm for computing generalized ranks of persistence modules using unfolding to zigzag modules, with applications in algebraic topology and data analysis.

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

Applied Algebraic Topology Network

Harder-Narasimhan Filtrations of Persistence Modules

Explore Harder-Narasimhan types in quiver representations, examining their applications and limitations in persistence modules across various contexts in algebraic topology.

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

Applied Algebraic Topology Network

Parallel Decomposition of Persistence Modules Through Interval Bases

Explore parallel decomposition of persistence modules using interval bases, enhancing Topological Data Analysis with distributed computation and Hodge decomposition techniques.

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

Applied Algebraic Topology Network

Homological Algebra for Persistence Modules

Introduction to persistence modules in algebraic topology, exploring tensor products, Hom operations, and their role in homological algebra. Insights into preserving exact sequences and advanced concepts.

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

Applied Algebraic Topology Network

On the Algebraic Geometry of Spaces of Persistence Modules

Explore algebraic geometry's application to persistence modules in topological data analysis, offering insights into data structure and shape analysis.

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

INI Seminar Room 2

Harder-Narasimhan Filtrations of Persistence Modules

Delve into Harder-Narasimhan filtrations and their applications in Topological Data Analysis, exploring quiver representations, skyscraper invariants, and their relationship with rank invariants.

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

Applied Algebraic Topology Network

Barcode Matchings and p-Norms of Persistence Modules

Explore the theory of matchings in one-parameter persistence, examining their relationship with persistence barcodes and distances. Delve into morphisms of persistence modules, comparing induced matchings with alternative approaches.

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

Applied Algebraic Topology Network

Bounds on the Interleaving Distance Between n-Parameter Persistence Modules

Explore polynomial-time bounds for interleaving distance between n-parameter persistence modules using loss functions, with applications in topological data analysis.

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

Applied Algebraic Topology Network

L-P Metrics on Multiparameter Persistence Modules

Explores generalizations of p-Wasserstein distance for multi-parameter persistence modules, introducing d_I^p and d_M^p metrics. Examines their properties and applications in topological data analysis.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Ephemeral Persistence Modules and Distance Comparison

Exploring sheaf theoretic methods in persistent homology, comparing approaches using Alexandrov's and gamma-topology, and examining pseudo-distances in persistence module spaces.

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

Applied Algebraic Topology Network

Oliver Vipond - Local Equivalence of Metrics for Multiparameter Persistence Modules

Explore local equivalence of metrics for multiparameter persistence modules, focusing on fibered bar codes' discriminative power and stability in topological data analysis.

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

Applied Algebraic Topology Network

Rachel Levanger - A Comparison Framework for Interleaved Persistence Modules

Explore rigorous tracking of noise in persistent homology, comparing approximation techniques and addressing non-uniform sub-level set filtrations in topological data analysis.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

David Meyer - Some Algebraic Stability Theorems for Generalized Persistence Modules

Algebraic stability theorems for generalized persistence modules, exploring interleaving metrics, bottleneck metrics, and isometry theorems in the context of poset algebras and quiver representations.

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