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#Geometric Topology

Showing: 36 courses
University of Chicago Department of Mathematics

Anosov Flows on 3-Manifolds

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Dive into Anosov flows on 3-manifolds, exploring their chaotic yet stable nature, classification challenges, and recent advancements in low-dimensional geometric topology.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 14

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Explore advanced concepts in topology with Bruno Zimmerman, delving into complex mathematical structures and their properties in this comprehensive lecture.
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1 Lesons
1 hour 34 minutes
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Free-Video
Hausdorff Center for Mathematics

Homeomorphisms of Euclidean Space

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Explore recent advances in understanding the topological group of homeomorphisms of Euclidean space, including methods and emerging conjectures in geometric topology.
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1 Lesons
42 minutes
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Free-Video
IMSA

Combinatorial Geometry Workshop - Lecture by Paul Bressel

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Explore combinatorial geometry concepts in this workshop led by Paul Bressel. Gain insights into advanced mathematical techniques and their applications in geometric problem-solving.
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1 Lesons
58 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Constructing Knots with Specified Geometric Limits

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Explore constructive proofs for geometric limits of knot complements using circle packings on conformal boundaries of tame hyperbolic 3-manifolds, with insights on related open questions.
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1 Lesons
52 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Geometric Objects Associated to Planar Bipartite Graphs

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Explore topological and geometric data associated with planar bipartite graphs, including knots, cluster varieties, and critical varieties, and their interconnections.
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1 Lesons
50 minutes
On-Demand
Free-Video
IMSA

Best Lipschitz Maps and Transverse Measures - Part 2

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Explores best Lipschitz maps between hyperbolic surfaces, focusing on approximation methods, transverse measures, and their connection to infinitesimal earthquakes in Teichmüller theory.
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1 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Disk Configuration Spaces and Topological Complexity

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Exploring disk configuration spaces, their topology, and topological complexity, focusing on ordered configurations of unit-diameter disks in infinite strips and their geometric implications.
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1 Lesons
51 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Coxeter Groups are Biautomatic - Lecture 2

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Explore Coxeter groups' biautomatic properties in this advanced geometric group theory lecture, part of a workshop fostering research collaboration and exposure to active areas in the field.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Fields Institute

Bordism of Derived Orbifolds - Lecture 3

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Explore advanced mathematical concepts in bordism theory and derived orbifolds with Stanford University expert Mohammed Abouzaid in this Fields Institute lecture.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Fields Institute

Triangulated Spheres and Their Double Homology

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Explore double homology of triangulated spheres in this mathematical talk, delving into advanced topological concepts and their applications in toric geometry.
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1 Lesons
42 minutes
On-Demand
Free-Video
Fields Institute

A Generalization of Polyhedral Products

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Explore advanced concepts in algebraic topology, focusing on a novel generalization of polyhedral products and their applications in toric topology and geometry.
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1 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

An Introduction to Polyhedral Products

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Explore the foundations of polyhedral products in this graduate-level lecture, covering key concepts and applications in toric topology and geometry.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Schmutz-Thurston Duality in Mapping Class Group-Equivariant Cell Decompositions

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Explore mapping class group-equivariant cell decompositions of Teichmueller space, focusing on Schmutz and Thurston's work for closed compact surfaces without marked points.
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1 Lesons
51 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Shear Coordinates of Weil-Petersson Circle Homeomorphisms

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Explore shear coordinates of Weil-Petersson circle homeomorphisms in this advanced mathematics lecture by Yilin Wang, delving into geometric and dynamic aspects of the topic.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Geometry of Diagram Groups

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Explore the geometry of diagram groups in this advanced mathematical lecture, delving into discrete mathematics and computer science concepts.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

The Geometry of Random Genus-0 Hyperbolic Surfaces via Trees

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Explore the geometry of random genus-0 hyperbolic surfaces through tree structures in this advanced mathematical lecture by Timothy Budd.
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1 Lesons
58 minutes
On-Demand
Free-Video
Isaac Newton Institute for Mathematical Sciences

Left-orderability and 3-manifold Groups - Rothschild Lecture

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Explore the connection between left-invariant total order in fundamental groups and geometric/analytic properties of 3-manifolds in this advanced topology lecture.
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1 Lesons
1 hour
On-Demand
Free-Video
Tom Rocks Maths

Klein Bottles - Alternative Visualizations and Misconceptions

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Explore alternative visualizations of Klein Bottles with mathematician Moira Chas, challenging conventional understanding and revealing surprising mathematical insights.
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1 Lesons
16 minutes
On-Demand
Free-Video
Renzo Ricca

The Beautiful Interplay of Topology and Physics

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Explore the fascinating connection between topology and physics, uncovering how mathematical concepts shape our understanding of the physical world.
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1 Lesons
44 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

The Geometric Ideas of René Thom Related to Manifolds with Singularities

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Explore René Thom's groundbreaking papers on transversality, cobordism, and manifolds with singularities, revealing their geometric insights and impact on mathematical understanding.
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1 Lesons
51 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Regularising Manifolds Using Ricci Flow

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Explore Ricci flow's applications in deforming and regularizing manifolds, including its use in identifying topology and proving geometric theorems.
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1 Lesons
47 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Waists Measured via Urysohn Width in Riemannian Manifolds

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Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension

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Explore nonnegative Ricci curvature, nilpotency, and Hausdorff dimension in relation to universal covers, minimal representing loops, and asymptotic cones of manifolds.
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1 Lesons
1 hour 1 minute
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Free-Video
Centre de recherches mathématiques - CRM

Orderability of 3-Manifold Groups and the L-Space Conjecture

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Explore orderability of 3-manifold groups, focusing on the L-space conjecture and its connections to group orderability, taut foliations, and Heegaard Floer homology in hyperbolic 3-manifolds.
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1 Lesons
56 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Rank of 3-Manifold Groups - Lecture 3

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Explore 3-manifold group ranks, covering Heegaard genus, Abert-Nikolov's work on rank growth, and geometric decompositions of hyperbolic 3-manifolds with bounded rank.
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1 Lesons
51 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Rank of 3-Manifold Groups - Part I

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Explore 3-manifold group ranks, covering generation, Heegaard genus, growth in cover towers, mapping tori, and geometric decompositions of hyperbolic 3-manifolds.
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1 Lesons
57 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Endperiodic Maps via Pseudo-Anosov Flows

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Explore atoroidal, endperiodic maps on infinite-type surfaces through pseudo-Anosov flows, examining stretch factors, foliation cones, and entropy functions in topological dynamics.
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1 Lesons
51 minutes
On-Demand
Free-Video
BIMSA

Quantitative Cobordism - Exploring Topology and Geometry

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Explore quantitative cobordism in topology, focusing on non-constructive existence proofs and connections to geometry. Delve into Manin's principle, Cheeger-Gromov heuristic, and manifold constructions.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Dense Embeddings of Hyperbolic Manifold Groups

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Explore dense embeddings of hyperbolic manifold groups, focusing on amalgamated products and linear Lie groups. Learn strategies to control properties of output embeddings.
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1 Lesons
41 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Profinite Properties of Finite-Volume Hyperbolic 3-Manifold Groups

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Explore profinite rigidity of finite-volume hyperbolic 3-manifold groups, examining volume, invariant trace fields, and arithmeticity as profinite invariants in geometric topology.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

A Combinatorial Characterization of Geometric 3-Manifolds - Lecture

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Explore geometric 3-manifolds through combinatorial characterization, focusing on Thurston geometries and their local combinatorial definitions. Learn about new algorithms for geometric decomposition.
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1 Lesons
52 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

An Approach to Simon's Conjecture

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Explore fundamental group epimorphisms between 3-manifolds and their implications for knot genera. Investigate conjectures related to Simon's conjecture in knot theory.
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1 Lesons
51 minutes
On-Demand
Free-Video
BIMSA

Ricci Limit Spaces are Semi-Locally Simply Connected

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Explore Ricci limit spaces and their semi-local simple connectivity, delving into fundamental groups and Gromov-Hausdorff convergence of Riemannian manifolds.
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1 Lesons
41 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

ナノフォトニクスおよびトポロジカルサイエンスの融合：光に対する人工ゲージポテンシャル - 2017年

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Dive into トポロジカルサイエンスとナノフォトニクスの融合研究、人工ゲージポテンシャルを用いた光制御の革新的アプローチと、オンチップ・フォトニック回路への応用可能性について探究する。
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1 Lesons
39 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Dehn-Filling-Like Quotients of Mapping Class Groups

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Explore Dehn-filling-like quotients of mapping class groups, examining their algebra and geometry, inspired by Thurston's hyperbolic Dehn filling theorem.
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1 Lesons
45 minutes
On-Demand
Free-Video