Regularising Manifolds Using Ricci Flow
Explore Ricci flow's applications in deforming and regularizing manifolds, including its use in identifying topology and proving geometric theorems.
Waists Measured via Urysohn Width in Riemannian Manifolds
Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.
Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension
Explore nonnegative Ricci curvature, nilpotency, and Hausdorff dimension in relation to universal covers, minimal representing loops, and asymptotic cones of manifolds.
Orderability of 3-Manifold Groups and the L-Space Conjecture
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.
Rank of 3-Manifold Groups - Lecture 3
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.
Rank of 3-Manifold Groups - Part I
Explore 3-manifold group ranks, covering generation, Heegaard genus, growth in cover towers, mapping tori, and geometric decompositions of hyperbolic 3-manifolds.
Endperiodic Maps via Pseudo-Anosov Flows
Explore atoroidal, endperiodic maps on infinite-type surfaces through pseudo-Anosov flows, examining stretch factors, foliation cones, and entropy functions in topological dynamics.
Quantitative Cobordism - Exploring Topology and Geometry
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.
Dense Embeddings of Hyperbolic Manifold Groups
Explore dense embeddings of hyperbolic manifold groups, focusing on amalgamated products and linear Lie groups. Learn strategies to control properties of output embeddings.
Profinite Properties of Finite-Volume Hyperbolic 3-Manifold Groups
Explore profinite rigidity of finite-volume hyperbolic 3-manifold groups, examining volume, invariant trace fields, and arithmeticity as profinite invariants in geometric topology.
A Combinatorial Characterization of Geometric 3-Manifolds - Lecture
Explore geometric 3-manifolds through combinatorial characterization, focusing on Thurston geometries and their local combinatorial definitions. Learn about new algorithms for geometric decomposition.
An Approach to Simon's Conjecture
Explore fundamental group epimorphisms between 3-manifolds and their implications for knot genera. Investigate conjectures related to Simon's conjecture in knot theory.
Ricci Limit Spaces are Semi-Locally Simply Connected
Explore Ricci limit spaces and their semi-local simple connectivity, delving into fundamental groups and Gromov-Hausdorff convergence of Riemannian manifolds.
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
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。
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.