Persistent Stiefel-Whitney Classes
Explore persistent Stiefel-Whitney classes in topological data analysis, extending beyond homology groups to estimate vector bundle structures from finite samples using a persistent approach.
Topological Complexity for Manifolds with Abelian Fundamental Group
Explores conditions for nonmaximal topological complexity in manifolds with abelian fundamental groups, generalizing results on spaces with small fundamental groups and nonorientable surfaces.
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.
Bredon Cohomology and LS-Categorical Invariants
Explore Bredon cohomology's role in estimating topological complexity of aspherical spaces and its application to equivariant LS-category of groups with operators.
Homology Inference for the Degree-Rips Bifiltration
Explore density-sensitive degree-Rips bifiltration, its homology inference framework, and applications to annular point clouds with outliers. Analyze homotopy types and explanatory power in topological data analysis.
The Topological Complexity of Pure Graph Braid Groups Is Stably Maximal
Explore the topological complexity of configuration spaces in graphs, using group theoretic estimates for higher topological complexity instead of traditional cohomology approaches.
Krystyna Kuperberg - Shape Theory: Vietoris-Cech Approach to Homotopy
Explore shape theory's geometric approach to homotopy for compact metric spaces, extending Vietoris' work on first homotopy groups to higher dimensions with applications in mind.
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.
Extremal Spherical Polytopes and Borsuk's Conjecture
Explore extremal spherical polytopes and their connection to Borsuk's Conjecture, delving into geometric principles and mathematical theories in this insightful presentation.
Claudia Landi - Multi-parameter Persistence from the Viewpoint of Discrete Morse Theory
Explore multi-parameter persistence through discrete Morse theory, connecting combinatorial properties of critical cells to algebraic properties of persistence modules in topological data analysis.
Lower Multiplicity Bounds via Classifying Spaces
Explore equivariant methods and classifying spaces to analyze Lusternik-Schnirelmann category variations, focusing on open covers with fundamental group constraints and applications to amenable subgroups.
Homology of Sliding-Squares Configuration Spaces
Explore homology of sliding-squares configuration spaces, comparing point and square configurations in planes and rectangles. Discover surprising growth patterns in homology group ranks.
Gromov-Hausdorff Distances, Borsuk-Ulam Theorems, and Vietoris-Rips Complexes
Explore Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes in geometry. Learn about recent advancements in lower bounding distances between spheres using innovative mathematical techniques.
Michael Farber - Topological Complexity of Spherical Bundles
Explore parametrized motion planning algorithms and the topological complexity of sphere bundles, examining characteristic classes and specific examples in applied algebraic topology.
Persistent Homotopy Groups of Metric Spaces
Exploring persistent homotopy groups of metric spaces, blending topology and geometry to capture dataset features beyond persistent homology, with applications and stability properties.
Linear Obstacles in Linear Systems and Ways to Avoid Them
Explore topology in control theory, focusing on obstacle-avoiding paths and cohomology rings using homotopy limits. Gain insights into theoretical computer science applications.
Parametrized Topological Complexity of Hyperplane Arrangement Bundles
Exploring parametrized motion planning in hyperplane arrangement bundles, focusing on topological complexity under supersolvability conditions. Joint work with Dan Cohen.
Robert Adler Interviewed by Omer Bobrowski
Insightful interview exploring Robert Adler's contributions to applied algebraic topology, offering valuable perspectives on the field's development and future directions.
The Gromov-Hausdorff Distance Between Spheres
Explore upper and lower bounds for Gromov-Hausdorff distances between spheres, including optimal correspondences and topological concepts related to the Borsuk-Ulam theorem.
Extracting Persistence Features with Hierarchical Stabilisation
Explore hierarchical stabilisation for extracting stable invariants from persistence modules, focusing on the stable rank and its applications in data analysis and classification tasks.
Enabling a Machine to Sense Geometry
Explore how to construct a reach space of kernels on persistent modules, enabling machine intelligence to sense geometry, with applications in synthetic and real scenarios.