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.
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.
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.
An Approximate Nerve Theorem
Explore the Nerve Theorem's application in topological data analysis, focusing on epsilon-acyclic covers and their impact on persistent homology approximations in space filtrations.
David Meyer - Some Algebraic Stability Theorems for Generalized Persistence Modules
Algebraic stability theorems for generalized persistence modules, exploring interleaving metrics, bottleneck metrics, and isometry theorems in the context of poset algebras and quiver representations.
Constructions of K-Regular Maps Using Finite Local Schemes
Explore k-regular maps and interpolation theory in algebraic geometry. Learn construction methods, bounds, and applications to continuous function interpolation using advanced mathematical concepts.
Bedlewo- Topological Complexity and the Motion Planning Problem in Robotics
Explore topological complexity in robotics motion planning, its algebraic topology properties, recent developments, and research trends in this rich field.
Pavle Blagojević - Bedlewo: Shadows of Cohen's Vanishing Theorem
Explore Cohen's Vanishing theorem and its applications in algebraic topology, geometry, and combinatorics. Discover its impact on configuration spaces and measure partition problems.
Michael Lesnick - Algebraic Stability of Zigzag Persistence Modules
Explore algebraic stability in zigzag persistence modules, covering key concepts, theorems, and applications in topological data analysis and computational topology.
Sheaf Based Modeling of Wireless Communications
Explore sheaf-based modeling for wireless communications, covering topology, simplicial complexes, interference, and network activation. Learn about persistence, homological invariants, and simulation examples.
Larry Wasserman - Robust Topological Inference
Explore robust topological inference with Larry Wasserman, covering persistence, confidence bands, bootstrap methods, and optimal tuning for data analysis and statistical modeling.
Matthew Kahle - Topology of Configuration Spaces of Hard Spheres
Explore configuration spaces, homology, and topology in hard sphere systems. Learn about critical points, computational approaches, and theoretical foundations in applied algebraic topology.
Tamal Dey - A Framework for Topological Summarization
Explore topological summarization frameworks, covering concepts like nerve complexes, multiscale mapper, persistence diagrams, and stability in hierarchical covers. Gain insights into advanced computational topology techniques.