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.
Musing About Robotic Football
Explore robotic football strategies, discussing modeling, non-fibrations, speed, sensing, and topological complexity in the context of navigating blockers to score.
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.
Nonlinear Dynamics in an Age of Heuristic Science
Explore nonlinear dynamics through combinatorial topology, offering efficient computational methods and new perspectives for multiscale systems and data-driven science in biology and engineering.
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.
Ling Zhou - Persistent Homotopy Groups of Metric Spaces
Explore persistent homotopy groups of metric spaces, covering discrete fundamental groups, stability theorems, and persistent rational homotopy in this advanced topology lecture.
Nathanael Cox - Effective Algorithms for Quotients of Semi-Algebraic Equivalence Relations
Explore efficient algorithms for computing quotients of semi-algebraic equivalence relations, focusing on complexity, tools, and key results in applied algebraic topology.
Tomoo Yokoyama - Generalizations of Morse Graph of Flows and Reeb Graph of Hamiltonian Flows
Generalizations of Morse and Reeb graphs for flows, exploring connections between dynamical systems, topological structures, and abstract orbit spaces. Insights into Conley theory and topological invariants.
Takashi Owada - Limit Theorems for Topological Invariants of the Dynamic Multi-Parameter Simplicial Complex
Explore topological invariants in dynamic multi-parameter simplicial complexes, covering connectivity, probability, and limiting processes in applied algebraic topology.
An Upper Bound on the Topological Complexity of Discriminantal Varieties
Explore upper bounds on topological complexity of discriminantal varieties, with applications to configuration spaces. Combines Morse theory, equivariant homotopy theory, and complex geometry.
Vanessa Robins Interviewed by Elizabeth Bradley
Explore applied topology with Vanessa Robins as she discusses her career journey, research interests, and insights on granular materials, collaborations, and emerging areas in the field.
Henry Adams - Fair Division
Explore how Sperner's lemma and topology can solve fair rent division among roommates with differing preferences, based on research and a New York Times article.
Moduli Spaces of Morse Functions for Persistence
Exploring Morse functions on surfaces, focusing on decomposition, elementary moves, and embeddings. Insights into persistence barcodes and the inverse problem through nesting posets of level sets.
Homological Percolation: The Formation of Giant Cycles
Explore homological percolation, analyzing giant cycles in random structures and their phase transitions. Learn to differentiate signal from noise in persistence diagrams and discover connections to Euler characteristic curves.
Parameterized Complexity of Quantum Invariants of Knots
Explore quantum invariants of knots, their parameterized complexity, and efficient algorithms for computation using graphical calculus and tree embeddings.
The Magnitude of a Metric Space
Explore the magnitude of metric spaces, an isometric invariant encoding volume, dimension, and capacity. Learn about current research and its connection to persistent homology.
Modeling and Replicating Persistence Diagrams
Explore modeling and replicating persistence diagrams for statistical inference in topological data analysis. Learn about RST approach, parametric modeling, and improvements for clustered data.
Erica Flapan - Topological and Geometric Symmetries of Molecular Structures
Explore topological and geometric approaches to studying symmetries of complex molecular structures, aiding chemists in verifying synthesized molecules' forms through experimental data interpretation.
Bernd Sturmfels - Learning Algebraic Varieties from Samples
Explore algebraic varieties through sampling, focusing on topology and geometry. Learn algorithms for determining dimensions and polynomials, with practical applications in Julia.
Rachel Levanger - A Comparison Framework for Interleaved Persistence Modules
Explore rigorous tracking of noise in persistent homology, comparing approximation techniques and addressing non-uniform sub-level set filtrations in topological data analysis.