Dmitri Burago: A Mozaic from Geometry, Dynamics, PDEs, and Maybe More
Explore unsolved problems and recent progress in geometry, dynamics, and PDEs through a mosaic of interconnected topics, featuring insights from collaborative research.
Saecular Persistence
Explore saecular persistence, a method to decompose persistence modules with non-field coefficients. Learn about applications in topology, generalized persistence diagrams, and scientific data analysis.
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.
Multiscale Many-body Correlations and Structure in Chemistry Data
Integrating graphs, topology, and geometry to analyze complex chemistry data, providing insights into multiscale correlations and structures beyond traditional methods.
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.
Configurations Spaces of Particles - Homological Solid, Liquid, and Gas
Exploring configuration spaces of particles with thickness, examining topological aspects of phase transitions in hard-sphere systems, and their implications for physics and mathematics.
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.
Looking for Geometry in the Supreme Court
Exploring geometric approaches to analyze U.S. Supreme Court voting behavior, discussing recent investigations using planar geometry and phylogenetic trees, and suggesting future directions in topology and geometry.
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.