Polyhedral Products in Motivic Homotopy Theory
Explore polyhedral products in motivic homotopy theory, delving into advanced mathematical concepts and their applications in algebraic topology and geometry.
Steenrod's Problem for Face Rings
Explore Steenrod's Problem in face rings, delving into advanced algebraic topology concepts and their applications in toric topology and polyhedral products.
A Generalization of Polyhedral Products
Explore advanced concepts in algebraic topology, focusing on a novel generalization of polyhedral products and their applications in toric topology and geometry.
Flag Complexes, Polyhedral Products and Geometric Group Theory
Explore connections between flag complexes, polyhedral products, and geometric group theory in this advanced mathematics lecture by Stephen Theriault from the University of Southampton.
Properties of Polyhedral Products
Explore properties of polyhedral products in this advanced mathematics lecture, covering key concepts and applications in toric topology and geometry.
The Davis-Januszkiewicz Construction Reinterpreted and Generalized
Explore a reinterpretation and generalization of the Davis-Januszkiewicz construction in toric topology, presented by Anthony Bahri from Rider University as part of the Graduate School on Toric Topology.
An Introduction to Polyhedral Products
Explore the foundations of polyhedral products in this graduate-level lecture, covering key concepts and applications in toric topology and geometry.
Topology and Dynamics of Higher-Order Networks - Lecture 1: General Introduction to Algebraic Topology on Networks and Simplicial Complexes
Explore algebraic topology in networks and simplicial complexes, focusing on homology and boundary operators. Gain insights into higher-order network structures and their impact on complex systems.
Topology and Dynamics of Higher-Order Networks - Lecture 2: Introduction to Algebraic Topology on Networks and Simplicial Complexes
Explore algebraic topology on networks and simplicial complexes, focusing on Hodge Laplacians and Dirac operators in higher-order networks. Gain insights into topological signals and their applications.
Multiscale Basis Dictionaries and Scattering Networks on Simplicial Complexes
Explore multiscale basis dictionaries and scattering networks on simplicial complexes, focusing on HGLET and GHWT. Learn applications in coauthorship/citation complex and article classification.
The High-Degree Rational Cohomology of the Special Linear Group
Explore high-degree rational cohomology of SL_n(Z) and SL_n(R) for number rings. Examine Steinberg modules and associated simplicial complexes to understand special linear group cohomology.
Waists Measured via Urysohn Width in Riemannian Manifolds
Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.
L^2 Cohomology of Buildings
Explore L^2 cohomology of buildings with Tadeusz Januszkiewicz, delving into advanced mathematical concepts and their applications in geometric group theory.
L^2 Homology of Groups and Consequences - Part I
Explore l^2 homology of groups, its definition via simplicial complex actions, and implications for group theory, particularly when these invariants vanish.
L^2 Homology of Groups and Consequences - Lecture 3
Explore l^2 homology of groups, its computation, and implications for group theory, focusing on cases where these invariants vanish.
L^2 Homology of Groups and Consequences - Lecture 2
Explore l^2 homology of groups through examples, calculations, and implications for group theory, focusing on vanishing invariants.
Triangulations of Manifolds and the Triangulation Conjecture
Explore the triangulation conjecture in topology, its validity in low dimensions, and its disproval in higher dimensions using advanced mathematical techniques.
Homology of Graphs and Hypergraphs
Explore topological structures of graphs and hypergraphs, including recent findings on homology and persistent homology, with applications in combinatorial and metric space analysis.
Topological Message Passing: From Graph Neural Networks to Simplicial Complexes on CW Networks
Delve into advanced Graph Neural Network concepts, exploring topological message passing, simplicial complexes, and high-dimensional interactions for computational graph networks and molecular design applications.
High-Dimensional Expanders - Lecture 2
Explore high-dimensional expanders with Irit Dinur, delving into advanced concepts and applications in analysis and theoretical computer science.
Low Dimensional Topology and Circle-Valued Morse Functions
Explore the Kakimizu complex for genus one hyperbolic knots, examining its structure, dimensions, and examples across various dimensions in 3-sphere topology.