Statistical Invariance of Betti Numbers in the Thermodynamic Regime
Explore statistical invariance of Betti numbers in random topology, examining conditions for topological inference through parametric statistics lens. Investigates asymptotic behavior and group invariance concepts.
Hardness Results in Discrete Morse Theory for 2-Complexes
Explore inapproximability and parameterized complexity in discrete Morse theory for 2-complexes, focusing on minimizing critical simplices and presenting new hardness results and an approximation algorithm.
A Limit Theorem for Betti Numbers of Random Simplicial Complexes
Explore asymptotic behavior of Betti numbers in homogeneous and spatially independent random simplicial complexes, extending previous work on Linial-Meshulam complexes using local weak convergence.
Andrew Thomas - Functional Limit Theorems for Euler Characteristic Processes
Explore functional limit theorems for Euler characteristic processes in Vietoris-Rips complexes, covering strong law of large numbers and central limit theorem in the thermodynamic regime.
Morse-Based Fibering of the Rank Invariant
Explore multi-parameter persistence in data analysis using discrete Morse theory to compute rank invariants, partition parameter space, and deduce persistence diagrams for equivalent classes of lines.
Sheaves as Computable and Stable Topological Invariants for Datasets
Explores sheaf theory in topological data analysis, connecting level-sets persistence with derived sheaves. Presents functorial equivalences, stability theorems, and barcode decompositions for continuous data analysis.
Borsuk-Ulam Theorems into Higher-Dimensional Codomains
Exploration of Borsuk-Ulam theorems in higher dimensions, generalizing results and discussing open questions related to optimal diameters and Schur polynomials.
Computing Minimal Persistent Cycles - Polynomial and Hard Cases
Explores computing minimal persistent cycles in algebraic topology, discussing polynomial and NP-hard cases, and presenting algorithms for weak pseudomanifolds with applications to scientific data analysis.
Oliver Vipond - Local Equivalence of Metrics for Multiparameter Persistence Modules
Explore local equivalence of metrics for multiparameter persistence modules, focusing on fibered bar codes' discriminative power and stability in topological data analysis.
Henry Adams and Enrique Alvarado - An Introduction to Morse Theory
Explore Morse theory's applications in topology, including CW complexes, key theorems, and simplification techniques, with real-world examples in material science.
How Math and AI Are Revolutionizing Biosciences
Exploring how mathematics and AI revolutionize biosciences, focusing on tackling challenges in biological data complexity, dimensionality, and nonlinearity to enhance AI's capabilities in drug design and viral mutation prediction.
Solving Systems of ODEs via Combinatorial Homological Algebra
Exploring efficient computation of homological representations in dynamical systems, with applications to differential equations and parameter space analysis.
Tverberg’s Theorem for Cell Complexes
Explore Tverberg's theorem generalization, homotopy decomposition of discretized configuration spaces, and topological extensions in this advanced algebraic topology discussion.
Effectual Topological Complexity
Explora la Complejidad Topológica Efectual, una nueva versión para G-Espacios. Aprende sus propiedades, relación con TC estándar y aplicación en superficies, especialmente en el toro.
Mikhail Katz - Collapsing Surfaces
Exploring surface collapse in Riemannian geometry, focusing on critical points, intersection theory, and Toponogov comparison. Analyzes fiber homotopy and discrete integration against Euler characteristic.
Topological Complexity Using Arbitrary Covers
Explore topological complexity using arbitrary covers, focusing on sectional category, ANRs, and generalized concepts. Gain insights into advanced algebraic topology techniques and applications.
Data Complexes, Obstructions, Persistent Data Merging
Explore data complexes, topological obstructions in database JOIN operations, and persistence levels in data alignment. Learn about measure theory, homotopy, and homology in the context of data integration.
Robert Ghrist - Laplacians and Network Sheaves
Explore cellular sheaves, Laplacians, and their applications in social networks and opinion dynamics. Learn about decentralized methods for computing sheaf cohomology and analyzing consensus and polarization.
The Gromov-Hausdorff Distance Between Spheres
Explore the Gromov-Hausdorff distance between spheres, its applications in geometry and topology, and methods for calculating precise values between specific sphere pairs.
Topological Complexity of Pure Graph Braid Groups
Explore topological complexity in graph braid groups, focusing on Farber's conjecture about ordered configuration spaces and its implications for topological robotics.
Luis Scoccola - Locally Persistent Categories & Metric Properties of Interleaving Distances
Explore locally persistent categories, metric properties of interleaving distances, and their applications in algebraic topology, including natural interleavings and weak equivalences.