Bounding the Interleaving Distance for Mapper Graphs with a Loss Function
Exploring interleaving distance for Mapper graphs, introducing a loss function to measure assignment quality and enable polynomial-time computation for data comparison and clustering.
Geometry and Complex Networks - A Powerful Partnership
Explore the intersection of geometry and complex networks, uncovering powerful applications in network science, data analysis, and modeling real-world systems.
Informational and Topological Signatures of Individuality in Network Neuroscience
Exploring brain function through topological data analysis, demonstrating improved individual and age discrimination using algebraic-topological features extracted from resting fMRI data compared to traditional methods.
Barcodes for the Topological Analysis of Gradient-Like Vector Fields
Explore topological analysis of gradient-like vector fields using barcodes. Learn about chain complexes, parametrization, and applications in smooth and discrete settings, with insights on stability and approximation.
Harmonic Persistent Homology for Disentangling Multiway Interaction in Data
Explore Harmonic Persistent Homology for analyzing multi-omics data, uncovering hidden patterns in complex diseases, and identifying biomarkers associated with latent biological pathways.
Teaching Neural Networks a Sense of Geometry
Explore Topological Data Analysis (TDA) and its intersection with machine learning to enhance neural networks' geometric reasoning abilities across various applications.
Detecting Non-Trivial Cycles of Point Clouds and Time Series Data on Manifolds
Explore techniques for identifying complex cycles in point clouds and time series data on manifolds, with applications in machine learning and dynamical systems.
Topological Node2vec: Improving Graph Embeddings with Persistent Homology
Exploring persistent homology to enhance graph embeddings, combining topology with machine learning for improved data analysis and representation in complex networks.
Efficient Spatial Insights - Landmark's Journey with Databricks and CARTO
Explore Landmark's transformation in spatial data analysis using Databricks and CARTO, reducing 10-day processes to 1 hour and enhancing decision-making across departments.
Persistent Homology for Infinite Complexes - Extending Theory to Infinite CW Complexes
Explore the extension of persistent homology to infinite CW complexes, including key theorems and applications in topological data analysis.
Tropical Vector Bundles and Matroids
Delve into advanced geometric concepts exploring toric vector bundles, matroids, and their tropical counterparts through classification, equivariant K-theory, and characteristic classes.
Introduction to Perverse Sheaves
Dive into the fundamental concepts and theoretical foundations of perverse sheaves with expert mathematician Mark Goresky, exploring advanced mathematical structures and their applications.
Quantitative Almost-Existence in Dimension Four
Delve into advanced symplectic geometry concepts, exploring Hofer-Zehnder's theorem and the existence of closed characteristics in four-dimensional space through rigorous mathematical analysis.
Sheaves on Graphs, the Hanna Neumann Conjecture, and Algebraic Geometry Applications
Explore advanced graph theory concepts through sheaf theory and the Hanna Neumann conjecture, featuring innovative problem-solving approaches and applications in discrete mathematics.
Spaces of Lorentzian Polynomials
Delve into advanced mathematical concepts exploring Lorentzian polynomials, their topology, and relationship with local Dressians, featuring insights on compactification and Tutte group connections.
Cohomologically Tropical Varieties and Mixed Hodge Structures
Delve into advanced geometric concepts exploring tropicalizations of torus subvarieties, focusing on Poincaré duality and mixed Hodge structures in relation to hyperplane arrangements.
Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 20
Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 4
Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 7
Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
A Second Course in Riemannian Geometry - Lecture 1
Delve into advanced Riemannian geometry concepts, exploring sophisticated mathematical principles and topological structures through expert-led instruction from a renowned mathematician.
Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 16
Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.