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.
Macroscopic Scalar Curvature and Local Collapsing
Exploration of macroscopic scalar curvature in Riemannian geometry, focusing on volume bounds for manifolds with hyperbolic metrics and collapsing techniques in metric geometry.
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.
Wasserstein Distances, Geodesics and Barycenters of Merge Trees
Explore computational frameworks for merge trees, including Wasserstein distances, geodesics, and barycenters. Learn efficient algorithms and applications in visualization, feature tracking, and ensemble clustering.
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.
Yevgeny Liokumovich - Urysohn Width, Isoperimetric Inequalities and Scalar Curvature
Explore metric spaces, Hausdorff measure, and continuous mappings. Discover connections to isoperimetric inequalities and Riemannian geometry's positive scalar curvature.
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.
Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions
Explore signed barcodes: a new visual representation for multi-parameter persistence modules, encoding rank invariants and enhancing exploration of complex topological structures.
Discrete Morse Theory Meets Multi-Parameter Persistence
Exploring connections between discrete Morse theory and multiparameter persistence in topological data analysis, focusing on critical cells, fibered rank invariant, and computational efficiency.
The Intrinsic Volumes of a Space Filling Diagram and Their Derivatives
Explore intrinsic volumes in molecular dynamics, focusing on space-filling diagrams and their derivatives. Learn formulas for weighted volumes and curvatures in Alpha shape representations.
Introduction to Stochastic Processes by Sanjib Sabhapandit
Explore stochastic processes in this advanced lecture, covering key concepts and applications in statistical physics for graduate-level students and researchers.
An Introduction to Spectral Data for Higgs Bundles
Explore spectral data for Higgs bundles, a key concept in algebraic geometry and mathematical physics, with insights on integrable systems and moduli spaces.
Population Genetics of Multiple Loci by Nick Barton
Explore population genetics theory and its applications in evolutionary processes, covering multiple loci analysis, quantitative predictions, and integration of mathematical and biological concepts.
Introduction to Nonlinear Dynamics - The Case of Catastrophe Theory by Vishwesha Guttal
Explore nonlinear dynamics and catastrophe theory in finance and macroeconomics. Learn alternative frameworks for analyzing modern financial systems and their economic impacts.
Dynamical Systems Applied to Biology - Part 1
Explore dynamical systems in biology, focusing on applications and mathematical approaches to understand complex biological processes and phenomena.
Symmetry in Topological Lattices
Explore symmetry in topological lattices with Fiona Burnell, delving into advanced mathematical concepts related to topological phases of matter in this graduate-level lecture.