Pawel Dlotko - A Few Simple Stories on Topology in Action
Explore practical applications of computational topology in material science, dynamical systems, and brain research. Learn how theory and algorithms work together to solve real-world problems.
Michael Lesnick - Algebraic Stability of Zigzag Persistence Modules
Explore algebraic stability in zigzag persistence modules, covering key concepts, theorems, and applications in topological data analysis and computational topology.
Tamal Dey - A Framework for Topological Summarization
Explore topological summarization frameworks, covering concepts like nerve complexes, multiscale mapper, persistence diagrams, and stability in hierarchical covers. Gain insights into advanced computational topology techniques.
Žiga Virk - Information Encoded in Persistence Diagrams
Explore topological data analysis through persistence diagrams, uncovering spatial properties like homology, geodesics, and proximity in various mathematical contexts.
Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances
Explore the mathematical foundations of persistence diagrams and their associated metrics, focusing on universality properties and distance calculations in topological data analysis.
RipsNet- Fast and Robust Estimation of Persistent Homology for Point Clouds
Estimating persistence diagrams of point clouds using neural networks for faster, more robust topological analysis. Overcomes computational complexity and sensitivity to outliers in practical applications.
Metric Geometry of Spaces of Persistence Diagrams
Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.
Spectral Relaxations of the Persistent Rank Invariant - Applied Algebraic Topology Network
Spectral relaxations of persistent rank invariant: A framework for continuous relaxations, offering stability and differentiability while preserving key properties and enabling efficient GPU-parallelized computation.