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#Homologies

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Simons Semester on Dynamics

Robustly Transitive Endomorphisms and Strong Volume Expansion for Toral Endomorphisms

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Dive into robust transitivity criteria for partially hyperbolic endomorphisms on the two-torus, exploring Blichfedt's theorem and its applications in dynamical systems.
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1 Lesons
49 minutes
On-Demand
Free-Video
Insights into Mathematics

An Introduction to Homology - Algebraic Topology

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Explore higher-dimensional topology through homology groups, cycles, and spanning trees. Learn to compute and characterize independent cycles in graphs using algebraic techniques.
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9 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Data Complexes, Obstructions, Persistent Data Merging

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Explore data complexes, topological obstructions in database JOIN operations, and persistence levels in data alignment. Learn about measure theory, homotopy, and homology in the context of data integration.
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24 Lesons
54 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Matthew Kahle - Topology of Configuration Spaces of Hard Spheres

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Explore configuration spaces, homology, and topology in hard sphere systems. Learn about critical points, computational approaches, and theoretical foundations in applied algebraic topology.
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25 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Sanjeevi Krishnan - Homological Programming

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Explore algebraic topology applications in programming, covering pursuit-evasion problems, positive cones, Alexander duality, and directed topology, with insights into decomposability and computational aspects.
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17 Lesons
57 minutes
On-Demand
Free-Video
Fields Institute

Eisenstein Cocycles and Values of L-Functions

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Explore Eisenstein cocycles, equivariant cohomology, and their applications to L-functions. Gain insights into recent constructions and their connections to theta kernels and arithmetic groups.
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16 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Computing Optimal Homotopies

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Explore optimal curve similarity measures using homotopy-based approaches, examining structural properties, algorithms, and open questions in topology and computational geometry.
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20 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Žiga Virk - Information Encoded in Persistence Diagrams

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Explore topological data analysis through persistence diagrams, uncovering spatial properties like homology, geodesics, and proximity in various mathematical contexts.
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13 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Fundamental Group of 2-Dimensional Random Cubical Complexes

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Explores fundamental groups in random 2D cubical complexes, analyzing their behavior and structure at different probability thresholds. Insights into topology and percolation theory.
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1 Lesons
27 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Antonio Rieser - Algebraic Topology for Graphs and Mesoscopic Spaces

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Explore algebraic topology for graphs and mesoscopic spaces, covering homotopy, homology, and metric cohomology. Learn about pseudotopological spaces and their applications in various mathematical categories.
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1 Lesons
54 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Torsion Homology Growth and Related Topics

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Explore torsion homology growth in compact CW complexes, examining Betti number growth in finite covers and connections to amenable category and minimal volume entropy.
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1 Lesons
52 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homology of Sliding-Squares Configuration Spaces

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Explore homology of sliding-squares configuration spaces, comparing point and square configurations in planes and rectangles. Discover surprising growth patterns in homology group ranks.
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1 Lesons
51 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 10

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Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 12

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Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 3

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Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.
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1 Lesons
1 hour 37 minutes
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Free-Video
ICTP Mathematics

Topology - Lecture 8

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Explore fundamental concepts and advanced techniques in topological spaces, manifolds, and algebraic topology with expert guidance from Bruno Zimmerman.
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1 Lesons
1 hour 36 minutes
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QuantumTopology

Homology of Jucys Murphy Elements and the Flag Hilbert Scheme

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Explore the intricate connections between Jucys-Murphy elements and flag Hilbert schemes, delving into their homological properties and algebraic structures.
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1 Lesons
47 minutes
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Free-Video
QuantumTopology

Homology of Yang-Baxter Operators and Search for (Co)Cycle Invariants of Knots

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Explore homology of Yang-Baxter operators and the quest for (co)cycle invariants in knot theory with mathematician Jozef Przytycki in this advanced topology lecture.
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1 Lesons
59 minutes
On-Demand
Free-Video
Insights into Mathematics

Introduction to Homology in Algebraic Topology - Part 2

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Explores cycles, boundaries, and homology in algebraic topology, focusing on graph modifications and using commutative group theory to analyze formal combinations of geometric elements.
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1 Lesons
41 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Steenrod Squares and Data Science - Exploring Connections in Algebraic Topology

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Explore the potential link between advanced algebraic topology concepts and data science classification, examining how increasing algebraic complexity may solve harder geometric problems.
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1 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

Homology of the Real Toric Varieties Associated with the Weyl Group of Types E7 and E8

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Explore the homology of real toric varieties linked to E_7 and E_8 Weyl groups in this advanced mathematical talk by Seonghyeon Yu from Ajou University.
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1 Lesons
17 minutes
On-Demand
Free-Video
Fields Institute

TQFTs and the Renaissance of the Algebraic Topology of Manifolds

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Explore the resurgence of algebraic topology in manifold studies, focusing on Topological Quantum Field Theories and their impact on modern mathematical research.
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1 Lesons
43 minutes
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Free-Video
Fields Institute

An Invitation to Graph Braid Groups

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Explore graph braid groups, from basic concepts to advanced topics like homology and polynomial growth, with insights on various graph types and their properties.
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12 Lesons
47 minutes
On-Demand
Free-Video
ICTP Condensed Matter and Statistical Physics

Topology and Dynamics of Higher-Order Networks - Lecture 1: General Introduction to Algebraic Topology on Networks and Simplicial Complexes

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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.
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1 Lesons
2 hours 16 minutes
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

Introduction to Lagrangian Fillings of Legendrian Links - Part 1

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Explore Lagrangian fillings of Legendrian links, their construction, and techniques to distinguish Hamiltonian isotopy classes. Delve into the connection with cluster algebras and key proof elements.
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3 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Poincaré Duality Fibrations and Graph Complexes

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Explore Poincaré duality fibrations and graph complexes in advanced mathematics. Gain insights from Alexander Berglund's conference talk at CIRM's thematic meeting on higher algebra, geometry, and topology.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Global Noncommutative Geometry Seminar

Ample Groupoids, Topological Full Groups, Algebraic K-Theory Spectra and Infinite Loop Spaces

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Explore ample groupoids, topological full groups, and their connections to algebraic K-theory spectra and infinite loop spaces in this advanced mathematics seminar.
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6 Lesons
58 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Cluster Duality and Non-Holomorphic Spectral Curves

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Explore cluster duality, geometric interpretations of tropical points, and their connections to local systems on curves through graphs, Lagrangian coverings, and affine group-valued local systems.
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9 Lesons
49 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Enumerative Geometry Through Sheaves

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Explore enumerative geometry, sheaf counting, and their applications in algebraic geometry. Discover new approaches to generalized Donaldson-Thomas invariants on Calabi-Yau threefolds.
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1 Lesons
1 hour
On-Demand
Free-Video
Stony Brook Mathematics

Real Loci of Non-Real Varieties - Mathematics Department Colloquium

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Explore cooriented submanifolds in real algebraic geometry, focusing on their properties, intersections, and linking numbers. Gain insights into the geometry of pencils and real projective spaces.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Banach Center

How Many Quivers Does a Knot Have? - Knots-Quivers Correspondence and Symmetries

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Explore knots-quivers correspondence, equivalent quivers classification, and implications for symmetric quiver invariants in knot theory.
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1 Lesons
45 minutes
On-Demand
Free-Video
BIMSA

Computing Differentials in the Adams Spectral Sequence and the Last Kervaire Invariant Problem

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Explore advanced methods for computing differentials in the Adams spectral sequence and uncover recent progress on the Last Kervaire Invariant Problem in dimension 126.
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1 Lesons
54 minutes
On-Demand
Free-Video
Banach Center

Knots and Categories

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Explore connections between knot theory and category theory, delving into mathematical concepts and their interrelationships in topology and algebra.
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1 Lesons
1 hour 24 minutes
On-Demand
Free-Video
Fields Institute

Correspondences, K-Theory and Homology for Étale Groupoids

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Explore advanced mathematical concepts in étale groupoids, focusing on correspondences, K-theory, and homology. Gain insights from expert Alistair Miller in this specialized seminar.
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1 Lesons
49 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Modeling Shapes and Fields - A Sheaf Theoretic Perspective

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Explore topological transforms for shape and field modeling, including Euler Characteristic and Lifted Euler Characteristic. Learn about sheaf theory in shape space construction and its applications in statistical analysis.
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1 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homology of Graphs and Hypergraphs

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Explore topological structures of graphs and hypergraphs, including recent findings on homology and persistent homology, with applications in combinatorial and metric space analysis.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institut Henri Poincaré

Laying Foundations for Very Large Scale Comparative Genomics

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Explore foundations for large-scale comparative genomics, focusing on techniques and challenges in analyzing vast genomic datasets across species.
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1 Lesons
30 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules

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Efficient algorithm for computing generalized ranks of persistence modules using unfolding to zigzag modules, with applications in algebraic topology and data analysis.
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1 Lesons
46 minutes
On-Demand
Free-Video
BIMSA

Gauge Fields and Categorification of Quantum Group Invariants of 3-Manifolds

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Explore new link and 3-manifold invariants associated with Verma modules of U_q(sl_N), their properties, and potential categorification in 3-manifold homology.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video