Homotopy Coherence - Theme and Variations
Explore homotopy coherence theory's evolution, applications, and links to representation theory in this semi-historical survey, offering unique insights and connections in algebraic topology.
Alexander Dranishnikov - On the LS-Category of Group Homomorphisms
Exploration of LS-category equality for group homomorphisms, discussing proofs for specific group classes and presenting a counterexample for geometrically finite groups.
Frédéric Chazal Interviewed by Steve Oudot
Entretien approfondi avec Frédéric Chazal, pionnier de la topologie appliquée, explorant son parcours, ses contributions majeures et sa vision pour l'avenir du domaine.
On the Weak Topological Complexity and the TC-Ganea Conjecture
Explores weak topological complexity and TC-Ganea conjecture, discussing conditions for spaces to satisfy TC(X x S^n)=TC(X)+TC(S^n) and presenting counterexamples to the conjecture.
Kathryn Hess Interviewed by Peter Bubenik - August 11, 2021
Engaging interview with mathematician Kathryn Hess, exploring her research, insights, and contributions to applied algebraic topology and related fields.
Cell Complex Neural Networks
Exploring neural network computations on cell complexes, generalizing graph neural networks and introducing inter-cellular message passing schemes that consider underlying topology.
Rips Complexes, Projective Codes, and Zeros of Odd Maps
Explore connections between Rips complexes, projective codes, and odd map zeros, bridging discrete geometry and topology. New insights into sphere Rips complexes' challenging nature.
Homotopic Distance and Generalized Motion Planning
Explore homotopic distance between maps, unifying Lusternik-Schnirelmann category and topological complexity. Learn how Morse-Bott functions and navigation functions apply to generalized motion planning problems.
Vietoris-Rips Complexes and Geometric Group Theory
Explore Vietoris-Rips complexes in geometric group theory, focusing on topological finiteness properties, hyperbolic groups, and recent developments in Morse theory and persistent homology.
Homotopy Types of Vietoris–Rips Complexes of Metric Gluings
Explore homotopy types of Vietoris-Rips complexes in metric wedge sums and gluings, with applications to persistent homology of metric graphs and insights into open research directions.
Approximate and Discrete Vector Bundles
Explore synchronization problems and dimensionality reduction through vector bundles. Learn how characteristic classes provide insights into global synchronization and data analysis challenges.
A Counter-Example to Hausmann's Conjecture
Explore a counter-example to Hausmann's conjecture on Vietoris-Rips complexes, challenging long-held beliefs in algebraic topology using persistent homology.
An Application of Discrete Morse Theory to Robot Motion Planning
Explore discrete Morse theory and its variants, learning how to apply this mathematical concept to develop continuous motion planning algorithms for autonomous devices.
Gunnar Carlsson Interviewed by Vin de Silva - February 3, 2021
Insightful interview with Gunnar Carlsson, exploring topics in applied algebraic topology and its applications in data analysis and machine learning.
On the Lusternik-Schnirelmann Theory of 4-Manifolds
Explore Lusternik-Schnirelmann category in 4-manifolds, focusing on covers, fillings, and Gay-Kirby trisections. Gain insights into decompositions of 4-manifolds into 1-handlebodies.
Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances
Explore the mathematical foundations of persistence diagrams and their associated metrics, focusing on universality properties and distance calculations in topological data analysis.
A Faithful Discretization of the Persistent Homology Transform
Explore a faithful discretization method for the Persistent Homology Transform, enhancing computational efficiency in topological data analysis and shape recognition.
Group Equivariant Non-Expansive Operators and Their Use in Deep Learning
Explore group equivariant non-expansive operators and their applications in deep learning, focusing on topological and geometrical properties.
A Theoretical Analysis of Quasiperiodicity Using Persistent Künneth Formulae
Explore quasiperiodicity through advanced mathematical analysis, focusing on persistent Künneth formulae and their applications in theoretical algebraic topology.
Interleaving by Parts for Persistence in a Poset
Explore interleaving techniques for persistence analysis in partially ordered sets, focusing on algebraic topology applications and methodologies.
A Topological Approach to Inferring the Intrinsic Dim. of Convex Sensing Data
Explore a topological method for determining the intrinsic dimension of convex sensing data, offering insights into data analysis and dimensionality reduction techniques.