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#Metric Geometry

Showing: 14 courses
Applied Algebraic Topology Network

Vietoris-Rips Thickenings - Problems for Birds and Frogs

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Explore open problems in Vietoris-Rips complexes, connecting diverse mathematical areas. Suitable for both broad theorists and problem-solving specialists in applied algebraic topology.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Macroscopic Scalar Curvature and Local Collapsing

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Exploration of macroscopic scalar curvature in Riemannian geometry, focusing on volume bounds for manifolds with hyperbolic metrics and collapsing techniques in metric geometry.
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1 Lesons
1 hour
On-Demand
Free-Video
Applied Algebraic Topology Network

The Gromov-Hausdorff Distance Between Spheres

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Explore upper and lower bounds for Gromov-Hausdorff distances between spheres, including optimal correspondences and topological concepts related to the Borsuk-Ulam theorem.
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1 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Urysohn Width

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Explore the 100-year history and applications of Urysohn width, a metric invariant quantifying space approximation by simplicial complexes. Discover its role in dimension theory and modern geometric challenges.
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1 Lesons
54 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Failure of the Curvature-Dimension Condition in Sub-Finsler Manifolds

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Explore the failure of curvature-dimension conditions in sub-Finsler manifolds, focusing on recent proofs and implications for sub-Riemannian geometry and the Heisenberg group.
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1 Lesons
40 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Vector-Valued Concentration on the Symmetric Group

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Explore vector-valued concentration inequalities for the symmetric group, examining implications for Banach space geometry and building on recent advancements in discrete hypercube analysis.
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1 Lesons
45 minutes
On-Demand
Free-Video
Banach Center

Distance, Curvature and Symmetry - A Haphazard Tour Through Metric Geometry

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Explore metric geometry through distance, curvature, and symmetry concepts, gaining insights into fundamental mathematical principles and their applications in spatial analysis.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
BIMSA

Sharp Stability for the Brunn-Minkowski Inequality for Arbitrary Sets

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Explore sharp stability in the Brunn-Minkowski inequality for arbitrary sets, delving into combinatorics and its connections with metric geometry and analysis.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
BIMSA

Filling Radius, Positive Scalar Curvature and Quantitative Operator K-Theory

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Explore techniques in quantitative operator theory to estimate filling radius, connecting positive scalar curvature and asymptotic dimension in large-scale geometry.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Packing Points in Projective Spaces

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Explore optimal point arrangements in projective spaces, surveying current research and open problems in this fundamental area of metric geometry with applications in digital communication.
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25 Lesons
47 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Alexandrov's Patchwork and the Bonnet-Myers Theorem for Lorentzian Length Spaces

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Explore global timelike curvature bounds in Lorentzian length spaces, examining Alexandrov's Patchwork analogue and Bonnet-Myers theorem applications for spacetime geometry.
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1 Lesons
31 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The Space of Causal Diamonds as a Lorentzian Pre-Length Space

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Explore causal diamonds in Mathematical Relativity, examining their geometry and geodesic structure when endowed with Hausdorff distance, and their implications for metric convergence stability.
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1 Lesons
41 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Non-Regular Spacetime Geometry via Metric Measure Geometry

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Explore non-regular spacetime geometry using metric geometry, extending Lorentzian geometry beyond classical differential geometry for low-regularity spacetimes and general spaces.
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1 Lesons
34 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Metric Geometry of Spaces of Persistence Diagrams

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Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.
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1 Lesons
46 minutes
On-Demand
Free-Video