Dehn-Filling-Like Quotients of Mapping Class Groups
Explore Dehn-filling-like quotients of mapping class groups, examining their algebra and geometry, inspired by Thurston's hyperbolic Dehn filling theorem.
Extensions of 1-Cocycles of the Mapping Class Group to the Ptolemy Groupoid
Explore extensions of 1-cocycles from mapping class groups to Ptolemy groupoids, delving into algebraic topology and Grothendieck-Teichmüller theory.
Perception of Visual Art and Topological Data Analysis
Explore topological data analysis applications in visual art perception, comparing eye movements for abstract paintings vs. AI-generated images using algebraic topology methods.
Persistent Homology of Plant-Pollinator Interactions - The Importance of Flowering Plant Surveys
Explore persistent homology in plant-pollinator interactions, analyzing topological features and the impact of flowering plant surveys on understanding community structures.
Metric Space Magnitude and Generalization in Neural Networks
Exploring metric space magnitude in neural networks: new topological complexity measures for assessing generalization capabilities, with applications to transformers and deep graph networks.
Harder-Narasimhan Filtrations of Persistence Modules
Explore Harder-Narasimhan types in quiver representations, examining their applications and limitations in persistence modules across various contexts in algebraic topology.
Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules
Efficient algorithm for computing generalized ranks of persistence modules using unfolding to zigzag modules, with applications in algebraic topology and data analysis.
Understanding Temporal Hypergraph Dynamics with Zigzag Persistence
Explore temporal hypergraphs and zigzag persistence to analyze complex systems' topological evolution, applied to cybersecurity and social networks for understanding underlying dynamics.
Spectral Relaxations of the Persistent Rank Invariant - Applied Algebraic Topology Network
Spectral relaxations of persistent rank invariant: A framework for continuous relaxations, offering stability and differentiability while preserving key properties and enabling efficient GPU-parallelized computation.
Bridging Persistent Homology and Discrete Morse Theory with Applications to Shape Reconstruction
Explore the connection between persistent homology and discrete Morse theory, unifying key concepts and applying insights to shape reconstruction in computational topology.
On Clustering scRNA-seq Data
Explore challenges and strategies in clustering single-cell RNA sequencing data, focusing on the k-cluster method's effectiveness for analyzing neuronal datasets in fruit flies.
From Topological to Quantum LDPC Codes - Lecture 4
Explore advanced concepts in quantum error correction, focusing on the transition from topological to quantum LDPC codes in this in-depth lecture.
Combinatorial Quantization and BV Structures of Moduli of Flat Connections - Part 2
Explore quantisation of moduli spaces through combinatorial methods and BV structures, focusing on flat connections in mathematical physics.
From Topological to Quantum LDPC Codes - Part 3
Explore advanced concepts in quantum error correction, focusing on the transition from topological to quantum LDPC codes in this in-depth lecture.
From Topological to Quantum LDPC Codes - Part II
Explore advanced concepts in quantum error correction, focusing on the transition from topological to quantum LDPC codes.
The Global Hecke Action - Talk 41
Delve into geometric Satake theory and explore how Rep(G^vee) actions on BunG sheaves integrate into global Hecke modifications, with applications in Betti, de Rham, and étale settings.
P-Form Symmetries in Functorial Quantum Field Theory
Explore p-form symmetries in functorial quantum field theory, focusing on implementing finite group global and gauged symmetries in TQFT using cohomology-decorated bordisms.
Riemann, Topology and Physics - Lecture 1
Explore interdisciplinary connections between Riemann geometry, topology, and physics in this doctoral-level lecture by Renzo Ricca at Beijing Institute of Technology.
Plumber's Algebra Structure on Symplectic Cohomology
Delve into advanced symplectic geometry concepts, exploring Plumber's PROP structures, nodal Riemann surfaces, and their applications to cohomological field theories and curve counting methods.
Compact Holonomy G2 Manifolds Need Not Be Formal
Delve into advanced mathematical concepts exploring why compact holonomy G_2 manifolds may not exhibit formality, challenging previous conjectures about special and exceptional holonomy manifolds.
Classification of Some Open Toric Domains
Delve into advanced symplectic geometry, exploring the classification of open toric domains in R4 and their symplectomorphic properties through S1-equivariant symplectic homology analysis.