Computing Optimal Homotopies
Explore curve similarity measures and homotopy-based deformations in GIS, medical imaging, and graphics. Survey geometric and topological metrics, algorithms, and open questions in optimal homotopy computation.
Heather Harrington - Multi-Parameter Persistent Homology and Applications
Explore multi-parameter persistent homology and its applications in topological data analysis, uncovering complex patterns and structures in high-dimensional datasets.
Bedlewo- On a Problem of Whitney and the Retract Theorem of Ważewski
Explores Whitney's inverted pendulum problem, its controversial solution, and the application of Ważewski's retract theorem to provide a rigorous mathematical argument for the original idea.
Topological Methods in Discrete Geometry - New Developments
Explores recent advancements in topological methods for discrete geometry, focusing on configuration spaces in cooperative game theory and their connections to embedding problems in Euclidean spaces.
Topological Complexity of Fibrations and Covering Maps
Explore topological complexity of fibrations and covering maps, examining their homotopy invariance and applications in robotics and mechanical device manipulation.
Solving Equations and Optimization Problems with Uncertainty
Explore algorithms for detecting zeros of imprecise continuous functions and approximating worst-case optima in optimization problems with uncertain feasible domains.
Kathryn Hess - Bedlewo: Topology Meets Neuroscience
Explore how topology applies to neuroscience across scales, from neurons to brain regions. Discover topological analysis of microconnectomes and neuron classification, with insights into brain imaging data.
Bedlewo - Topological Complexity of the Klein Bottle
Explore the topological complexity of non-orientable surfaces, focusing on the Klein bottle and extending findings to surfaces of genus ≥2. Collaborative research insights shared.
Crash Course in Riemannian Geometry by Harish Seshadri
Introductory lecture on Riemannian geometry, covering fundamental concepts and principles for graduate-level students in mathematics and theoretical physics.
Topology of Artificial Neuron Activations in Deep Learning
Explore the topology of artificial neuron activations in deep learning, from image classification to natural language processing, with insights on convolutional neural networks and transformer-based models.
Two Methods of Efficiently Approximating Semi-Algebraic Sets Up to Homotopy
Explores efficient methods for approximating semi-algebraic sets, focusing on singly exponential complexity algorithms and their applications in algebraic geometry.
Antonio Rieser - Algebraic Topology for Graphs and Mesoscopic Spaces
Explore algebraic topology for graphs and mesoscopic spaces, covering homotopy, homology, and metric cohomology. Learn about pseudotopological spaces and their applications in various mathematical categories.
Every Stable Invariant of Finite Metric Spaces Produces False Positives
Explore stable invariants in computational topology, their limitations in approximating Gromov-Hausdorff distance, and the inevitability of false positives when using Hilbert space-valued invariants.
Wanted- Topologists for Autonomous Robots Community
Exploring topological complexity in robotics: from path planning to task spaces. Insights into rigorous formulations for robotic autonomy, emphasizing environment topology and combinatorics in cooperative motion.
The Reeb Graph of a Smooth Function Encodes the Function Class and Manifold Type
Explore how Reeb graphs of smooth functions encode function class and manifold type, examining structures for Morse and Morse-Bott functions and their relationship to manifold properties.
Urs Lang - Combinatorial Dimension and Higher-Rank Hyperbolicity
Exploration of (n,δ)-hyperbolicity in metric spaces, its relation to Gromov's δ-hyperbolicity, and applications in geometric group theory and hierarchically hyperbolic groups.
On the Rational Topological Complexity of Coformal Elliptic Spaces
Explore rational topological complexity bounds for elliptic spaces, focusing on coformal cases where it aligns with rational homotopy dimension.
Recent Advances in Theory and Implementation of Multi-Parameter Persistence
Explores recent developments in multi-parameter persistence, covering stable filtrations and discrete descriptors. Includes interactive clustering software demo and discusses extensions of one-parameter persistence concepts.
The Lower Semi-Continuity of Pi_1 and Nilpotent Structures in Persistence
Explore lower semi-continuity of π₁ in non-compact spaces, examining symmetries and nilpotent structures in persistence theory for compact geodesic space sequences.
Configuration Spaces of Hard Squares
Exploring topology of configuration spaces with hard squares, focusing on Betti numbers' growth rate in confined regions. New insights into complex geometric arrangements.
Symmetric and Symmetrized Topological Complexity of the Torus
Explore symmetric and symmetrized topological complexity of the torus, completing the description for closed surfaces using obstruction theory and explicit resolution of integers over full braid group.