Ulrich Bauer - Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Rips Filtrations
Explore Gromov hyperbolicity, geodesic defect, and apparent pairs in Rips filtrations, extending Rips' results on contractibility and examining computational implications for persistent homology.
Bradley Nelson: Parameterized Vietoris-Rips Filtrations via Covers
Explore computational topology techniques for large filtered geometric complexes, focusing on Vietoris-Rips filtrations and cover-based methods for parallel computation and compression.
Luis Scoccola - Density-Sensitive and Robust Vietoris-Rips Filtrations
Explore density-sensitive and robust Vietoris-Rips filtrations in algebraic topology, including function-Rips, degree-Rips, and subdivision-Rips, with applications and open questions.
Shapes and Geometry of Surfaces by Mahan Mj
Explore the fascinating world of surfaces and their geometric properties. Learn about classification, topology, and curvature in this comprehensive lecture on shapes in space.
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.
Surfaces in 3-Manifolds and the Thurston Norm
Explore the Thurston norm in 3-manifold topology, its significance in measuring surface complexity, and its role in understanding modern topological breakthroughs.
Discrete Surface Geometry and Intrinsic Triangulations
Explore discrete surface geometry and intrinsic triangulations, bridging theory and algorithms in geometric computing. Learn about surface meshes, Gaussian curvature, and applications in robust geometry processing.
Herbert Edelsbrunner Interviewed by Dmitriy Morozov - September 30, 2020
Insightful interview with Herbert Edelsbrunner, exploring his contributions to computational geometry and topology, career journey, and perspectives on the field's evolution and future directions.
Algebraic Tools for Multiparameter Persistent Homology
Explore advanced algebraic techniques for analyzing multiparameter persistent homology, including primary decomposition and multigraded algebra, with examples and applications in topology.
Cohomological Characterization of Information Structures
Exploring cohomological methods to quantify statistical interactions in datasets, linking information theory, statistical physics, and machine learning for improved data analysis and interpretation.
Data Driven Torsion Coordinates and Wasserstein Stability
Explore data-driven torsion coordinates in finite Lens spaces, LPCA dimensionality reduction, and Wasserstein stability for topological data analysis and nonlinear dimensionality reduction.
The Fundamental Group of 2-Dimensional Random Cubical Complexes
Explores fundamental groups in random 2D cubical complexes, analyzing their behavior and structure at different probability thresholds. Insights into topology and percolation theory.
Borsuk–Ulam Theorems for Maps into Higher-Dimensional Codomains
Explore Borsuk-Ulam theorems for sphere maps to higher-dimensional spaces, examining topological properties and optimal diameter bounds for odd maps from S^n to R^k where k > n.
Comparative Stability of Two Zigzag Bottleneck Distances
Explores zigzag persistence in algebraic topology, comparing bottleneck distances for zigzag modules. Analyzes similarities and differences between approaches, focusing on Auslander-Reiten quiver perspective.
Every nD Persistence Module Is the Restriction of an (n+1)D Indecomposable Module
Explore a constructive process for building (n+1)D indecomposable modules from nD persistence modules, with insights on its implications and consequences.
Efficient Approximation of the Matching Distance for 2-Parameter Persistence
Explore efficient algorithms for approximating matching distance in 2-parameter persistence modules, focusing on quad-tree refinement and local adaptive bounds for improved computational performance.
Persistence-Based Skeletonization of Images
Explores algorithms for splitting images into convex polygons using topological persistence, including Convex Constrained Mesh and Persistent Resolution-Independent Mesh for edge detection.
From Large to Infinite Random Simplicial Complexes
Explore two models of random simplicial complexes extending the Erdos-Renyi model, examining their Alexander duality relation and the unique infinite Rado simplicial complex.
The Bulk and the Extremes of Online Minimal Spanning Acycles
Explores distributional properties of weights in random minimum spanning acycles, focusing on online settings. Examines bulk convergence to giant shadow measure and extremal convergence to inhomogeneous Poisson point process.
Geometry and Topology of Decision
Explore geometric and topological approaches to decision-making when faced with conflicting expert opinions, examining theoretical concepts and practical applications in various scenarios.
On a Canonical Construction of Tessellated Surfaces From Finite Groups
Explores a construction linking finite group multiplication tables to tessellated surfaces, discussing properties, group actions, and connections to classical mathematical constructions.