Mathematics - Algebraic Topology

Algebraic TopologyUnderstanding Directed Spaces and Their Distances

An overview of directed spaces, paths, and their significance in mathematics.

Lisbeth Fajstrup, Brittany Terese Fasy, Wenwen Li

2025-06-16T20:48:47+00:00 ― 6 min read

Category TheoryAn Introduction to Functor Double Categories

Explore functor double categories and their role in understanding complex relationships in mathematics.

Jaco Ruit

2025-06-16T20:22:34+00:00 ― 5 min read

Algebraic TopologyUnderstanding Up Persistent Laplacian in Data Analysis

A look at up persistent Laplacian in analyzing complex datasets.

Rui Dong

2025-06-15T07:40:22+00:00 ― 5 min read

Algebraic TopologyBifiltrations: A New Approach to Data Analysis

Exploring bifiltrations for improved data analysis and outlier management.

Michael Lesnick, Kenneth McCabe

2025-06-15T01:59:33+00:00 ― 4 min read

Algebraic TopologyAdapting Merge Trees for Periodic Structures in Material Science

A look at how merge trees enhance our grasp of crystalline materials.

Herbert Edelsbrunner, Teresa Heiss

2025-06-15T00:14:41+00:00 ― 5 min read

Category TheoryRozansky-Witten Models and Functorial Field Theory

Exploring Rozansky-Witten models and their significance in mathematics and physics.

Lorenzo Riva

2025-06-14T20:18:44+00:00 ― 4 min read

Machine LearningEvaluating Variational Autoencoders through Topological Degree

This research explores how topological degree assesses the effectiveness of VAEs in capturing data structure.

Mahefa Ratsisetraina Ravelonanosy, Vlado Menkovski, Jacobus W. Portegies

2025-06-13T08:55:11+00:00 ― 5 min read

Algebraic TopologyGroup Actions on Manifolds: Insights and Challenges

Exploring the relationships between groups and manifolds through the Nielsen realization problem.

Kaif Hilman, Dominik Kirstein, Christian Kremer

2025-06-13T00:10:51+00:00 ― 6 min read

Geometric TopologyFree Circle Actions on Manifolds

Exploring free circle actions and their implications on connected manifolds.

Yi Jiang, Yang Su

2025-06-12T10:38:08+00:00 ― 6 min read

Geometric TopologyThe Complexity of Manifolds: A Deep Dive

An overview of manifold classification and relationships in topology.

Csaba Nagy, John Nicholson, Mark Powell

2025-06-12T08:27:03+00:00 ― 5 min read

Algebraic TopologyA Deep Dive into Covering Spaces

Explore the significance of covering spaces in algebraic topology and their applications.

Jelle Wemmenhove, Cosmin Manea, Jim Portegies

2025-06-08T19:41:01+00:00 ― 6 min read

Computational ComplexityConnecting Graph Theory, Algebra, and Topology

A new approach to graph homomorphisms sheds light on complex problems.

Sebastian Meyer, Jakub Opršal

2025-06-04T15:37:24+00:00 ― 5 min read

Algebraic TopologyConnecting Persistence Diagrams and Schubert Calculus

This article explores the intersection of persistence diagrams and Schubert calculus for better data analysis.

Yasuaki Hiraoka, Kohei Yahiro, Chenguang Xu

2025-06-04T09:04:09+00:00 ― 5 min read

Symplectic GeometryClassifying Lagrangian Immersions in Symplectic Geometry

Examining cobordism groups and properties of Lagrangian immersions in symplectic manifolds.

Dominique Rathel-Fournier

2025-06-03T22:34:57+00:00 ― 4 min read

CombinatoricsUnderstanding Digraphs and Their Properties

Explore the relationships between digraphs, multipaths, and matroids.

Luigi Caputi, Carlo Collari, Sabino Di Trani

2025-06-03T21:42:31+00:00 ― 4 min read

Quantitative MethodsAnalyzing Turing Patterns in Chemical Systems

This article examines how Turing patterns form and are analyzed using topological data analysis.

Reemon Spector, Heather A. Harrington, Eamonn A. Gaffney

2025-06-03T20:45:24+00:00 ― 7 min read

Algebraic TopologyAn Introduction to Homotopy Theory

Learn about the basic concepts and applications of homotopy theory in mathematics.

Yuhang Wei

2025-06-03T16:01:42+00:00 ― 4 min read

Algebraic TopologyAn Introduction to Lie Groups and Algebras

Explore the fundamental concepts of Lie groups and algebras in mathematics and physics.

Arthur Garnier

2025-06-02T13:48:42+00:00 ― 5 min read

Algebraic TopologyUnderstanding Triviality in Stunted Projective Spaces

This article examines the triviality of stunted projective spaces in topology.

Sudeep Podder, Gobinda Sau

2025-06-02T00:42:12+00:00 ― 5 min read

CombinatoricsThe Intricacies of Simply Rooted Families and Cubical Sets

A look into simply rooted families and their connection to cubical sets.

Dhruv Bhasin

2025-06-01T23:23:33+00:00 ― 5 min read

Algebraic TopologyUnderstanding Hypergraphs and Their Homology

A look into hypergraphs and the role of homology in complex systems.

Ellen Gasparovic, Emilie Purvine, Radmila Sazdanovic

2025-06-01T13:46:47+00:00 ― 5 min read

Algebraic TopologyThe Geometry of Arrangements and Complements

A look into the relationships between shapes and their spaces in mathematics.

Vsevolod Tril

2025-06-01T10:17:03+00:00 ― 5 min read

Algebraic TopologyInsights into Motivic Homology

Exploring connections between geometric objects and algebraic structures.

Federico Ernesto Mocchetti

2025-05-31T16:22:10+00:00 ― 7 min read

Algebraic TopologyUnderstanding the Intricacies of Cubic Surfaces and Quartic Curves

A look at the complexities of cubic surfaces and quartic curves in geometry.

Weiyan Chen, Xing Gu

2025-05-28T17:39:38+00:00 ― 6 min read

ComputationInnovative Method for Isomorphism Checking in Factorial Designs

A new approach to determine isomorphism in Orthogonal Arrays using Topological Data Analysis.

Roberto Fontana, Marco Guerra

2025-05-27T07:53:22+00:00 ― 5 min read

CombinatoricsUnderstanding Coboundary Expansion

Learn about coboundary expansion and its impact on group dynamics.

Tali Kaufman, Izhar Oppenheim, Shmuel Weinberger

2025-05-25T16:04:44+00:00 ― 5 min read

Algebraic TopologyExploring the Dynamics of Modules in Algebra

A look into modules, their types, and how they interact in algebra.

Alex Elchesen, Amit Patel

2025-05-25T13:11:36+00:00 ― 7 min read

Algebraic TopologyUnderstanding Directed Graphs and Their Complexities

A look into directed graphs, flag complexes, and their relationships.

Thomas Chaplin, Heather A. Harrington, Ulrike Tillmann

2025-05-24T08:20:16+00:00 ― 6 min read

Symplectic GeometryPaths in a Unique Park: Understanding Connections

Explore the intriguing world of paths and their connections in a special park.

Vardan Oganesyan

2025-05-23T17:11:19+00:00 ― 5 min read

Algebraic TopologyUnderstanding Shapes Through Differential Forms

A look into how shapes behave using differential forms and cohomology.

Alice Petrov

2025-05-23T00:35:48+00:00 ― 5 min read

Algebraic TopologyUnpacking the Macías Topology

Discover the unique features and significance of Macías topology in mathematics.

Jhixon Macías, Reyes Ortiz

2025-05-22T14:29:50+00:00 ― 5 min read

Algebraic TopologyUnderstanding Configuration Categories in Mathematics

Learn how configuration categories help us organize and analyze arrangements in space.

Pedro Boavida de Brito, Geoffroy Horel, Danica Kosanović

2025-05-21T11:48:21+00:00 ― 5 min read

Algebraic TopologyAnalyzing Point Clouds with Persistent Homology

Learn how to analyze data represented as point clouds using persistent homology.

David Beers, Heather A Harrington, Jacob Leygonie

2025-05-20T19:12:50+00:00 ― 6 min read

Algebraic TopologyStudying Symplectic Groups Through Algebraic Arc Complexes

This paper explores stability in symplectic groups using algebraic arc complexes.

Ismael Sierra, Nathalie Wahl

2025-05-20T15:36:25+00:00 ― 4 min read

Algebraic TopologyUnderstanding Topological Data Analysis and Its Benefits

Learn how topological data analysis helps simplify complex data.

Jonathan M. Mousley, Paul Bendich

2025-05-17T12:56:36+00:00 ― 8 min read

Category TheoryOrganizing Game Night: A Mathematical Approach

Learn to arrange game night with concepts from monoidal bicategories.

Ettore Aldrovandi, Milind Gunjal

2025-05-15T16:06:28+00:00 ― 6 min read

Algebraic TopologyUnderstanding Homotopy Theory Through Model and Diagram Categories

A look into model categories, diagram categories, and their applications in mathematics.

Boris Chorny, David White

2025-05-15T04:53:56+00:00 ― 5 min read

Algebraic TopologyMeasuring Similarity with Topological Data Analysis

Discover how TDA helps classify sounds and shapes by measuring similarity.

Jiaxing He, Bingzhe Hou, Tieru Wu

2025-05-15T00:41:44+00:00 ― 5 min read

Algebraic TopologyAn Introduction to Coloured Partition Algebras

Learn how colored partition algebras group items in unique ways.

James Cranch, Daniel Graves

2025-05-13T03:51:36+00:00 ― 5 min read

Algebraic TopologyUnderstanding Motive Homotopy Theory

A look into the complexities of motive homotopy theory and its tools.

Hana Jia Kong, Weinan Lin

2025-05-11T09:49:36+00:00 ― 6 min read