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#Riemannian Geometry

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University of Chicago Department of Mathematics

Counting Closed Geodesics and Improving Weyl's Law for Predominant Sets of Metrics

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Dive into the behavior of closed geodesics and Weyl's law on compact manifolds. Explore predominance in Riemannian metrics and its implications for quantitative bounds in geometry.
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1 Lesons
54 minutes
On-Demand
Free-Video
Institute for Advanced Study

Geometry of 2-Dimensional Riemannian Disks and Spheres - Regina Rotman

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Explore 2D Riemannian geometry, focusing on disks and spheres. Learn about geodesics, sweep-outs, and curve shortening through examples and problem-solving.
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8 Lesons
1 hour
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

How Hard is the Theorem of Stolz - Metrics and Scalar Curvature in Spin Manifolds

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Delve into the complexity of Stolz's theorem on positive scalar curvature metrics, exploring metric deformations and manifold transformations through groundbreaking mathematical research findings.
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1 Lesons
1 hour 5 minutes
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Free-Video
ICTP Mathematics

Optimal Transportation, Monge-Ampère Equations and Riemannian Ricci Bounds - Lecture 3

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Explore geometric measure theory and optimal transport with a focus on Monge-Ampère equations and Riemannian Ricci bounds in this advanced mathematics lecture by L. Ambrosio.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Hyperbolization, Cubulation, and Applications in Negative Curvature Geometry

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Explore hyperbolization procedures, their impact on polyhedra, and the resulting manifolds' properties. Discover how fundamental groups interact with CAT(0) cube complexes in negatively curved spaces.
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1 Lesons
55 minutes
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Free-Video
The Royal Institution

The Extraordinary Theorems of John Nash

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Explore John Nash's revolutionary contributions to game theory and geometric analysis with Fields Medal winner Cédric Villani, delving into the world of mathematical genius and groundbreaking theorems.
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1 Lesons
1 hour
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Stable Adaptation and Learning in Nonlinear Systems and Neural Networks

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Explore nonlinear systems tools for insights on collective computation and learning in large dynamical networks, focusing on stable adaptation and implicit sparse regularization.
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1 Lesons
35 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Discrete Homotopy Theory and Applications

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Explore discrete homotopy theory's evolution, applications in topology, geometry, and group theory. Learn simplified approaches to fundamental groups and covering spaces, with insights into various mathematical domains.
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35 Lesons
49 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Geometry and Topology of Data

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Explore hyperconvexity and generalized curvature in metric spaces, linking topological data analysis with geometric concepts for a deeper understanding of data structures.
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1 Lesons
43 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 20

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 4

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 7

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
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1 Lesons
1 hour 24 minutes
On-Demand
Free-Video
Fields Institute

A Second Course in Riemannian Geometry - Lecture 1

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Delve into advanced Riemannian geometry concepts, exploring sophisticated mathematical principles and topological structures through expert-led instruction from a renowned mathematician.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 16

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 17

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 12

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric and topological structures through rigorous mathematical analysis and theoretical frameworks.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 23

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric and topological structures through expert-led mathematical discussions and theoretical frameworks.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 24

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric and topological structures through expert-led mathematical discussions and theoretical frameworks.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 19

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric structures and topological principles through expert-led mathematical discussions and theoretical frameworks.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 18

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric and topological structures through rigorous mathematical analysis and theoretical frameworks.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 9

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric structures and topological principles through expert-led mathematical discussions and theoretical frameworks.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 15

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led instruction from the Fields Institute.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 13

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric structures and topological principles through expert-led mathematical discussions and theoretical frameworks.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 11

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 5

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 8

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 2

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led instruction from the University of Waterloo.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 6

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Delve into advanced concepts of Riemannian geometry, exploring sophisticated mathematical principles and topological structures through expert-led mathematical discourse and theoretical frameworks.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 14

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric and topological structures through rigorous mathematical analysis and theoretical frameworks.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 10

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric and topological structures through rigorous mathematical analysis and theoretical frameworks.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 22

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric structures and topological principles through expert-led mathematical discussions and theoretical frameworks.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
Fields Institute

Topics in Geometry and Topology: A Second Course in Riemannian Geometry - Lecture 21

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Delve into advanced concepts of Riemannian geometry, exploring complex geometric structures and topological principles through expert-led mathematical discussions and theoretical frameworks.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Gromov-Hausdorff Distance Between Spheres

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Explore the Gromov-Hausdorff distance between spheres, its applications in geometry and topology, and methods for calculating precise values between specific sphere pairs.
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16 Lesons
58 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Geodesic Complexity of Riemannian Manifolds

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Explore geodesic complexity in Riemannian manifolds, connecting robot motion planning to topology and geometry. Learn about cut loci, bounds, and applications in this advanced mathematical talk.
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18 Lesons
1 hour 2 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Symmetric Spaces by Pralay Chatterjee

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Explore symmetric spaces in this advanced lecture on geometry, groups, and dynamics. Delve into modern research aspects and connect with cutting-edge theories in the field.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Crash Course in Riemannian Geometry by Harish Seshadri

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Introductory lecture on Riemannian geometry, covering fundamental concepts and principles for graduate-level students in mathematics and theoretical physics.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Curvature Bounds and the Length of the Shortest Closed Geodesic

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Explore upper bounds for shortest periodic geodesics on Riemannian manifolds, examining curvature's impact on closed geodesic length in various geometric contexts.
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1 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Yevgeny Liokumovich - Urysohn Width, Isoperimetric Inequalities and Scalar Curvature

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Explore metric spaces, Hausdorff measure, and continuous mappings. Discover connections to isoperimetric inequalities and Riemannian geometry's positive scalar curvature.
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1 Lesons
49 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 14

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Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in modern geometry.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 12

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Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in modern geometry and physics.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 11

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Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 10

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Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in modern geometry and physics.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
ICTP Mathematics

Hyperkähler Manifolds: An Introduction - Part 4.1

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Explore advanced concepts in complex geometry, focusing on Hyperkähler manifolds and their properties in this comprehensive mathematical lecture.
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1 Lesons
51 minutes
On-Demand
Free-Video
ICTP Mathematics

Dynamics of the Geodesic Flow on Surfaces Without Conjugate Points - Lecture 2

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Explore geodesic flow dynamics, maximal entropy measures, and Patterson-Sullivan measures on ideal boundaries in surfaces without conjugate points.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 19

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Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture by Claudio Arezzo.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 20

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Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in modern geometry and physics.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 17

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Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 15

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Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture by Claudio Arezzo.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 13

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Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Brunn-Minkowski Inequalities for Sprays on Riemannian Surfaces

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Generalization of Minkowski average on Riemannian manifolds, characterizing curve families on surfaces satisfying Brunn-Minkowski inequality. Explores conditions for constant-speed curves and geodesic curvature.
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1 Lesons
24 minutes
On-Demand
Free-Video
Mathemaniac

Exponentiating Vectors, Derivatives, and Vector Fields - Mathematical Concepts Explained

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Explore the concept of exponentiation applied to vectors, derivatives, and vector fields, uncovering connections between seemingly different mathematical ideas and their practical applications.
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5 Lesons
30 minutes
On-Demand
Free-Video
IMSA

Bifurcation Phenomena in Geometric Variational Problems

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Explore classical Bifurcation Theory and its modern applications in Riemannian Geometry, covering minimal and constant mean curvature surfaces and the Yamabe problem.
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1 Lesons
49 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

On the Regularity Implied by the Assumptions of Geometry

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Explore the theory of Regularity Transformation equations and their impact on non-regular spacetime geometry, including applications in General Relativity and Einstein-Euler equations.
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1 Lesons
46 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Kato Meets Bakry-Émery: Curvature Conditions in Riemannian Geometry

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Explore the relationship between Bakry-Émery curvature-dimension and Kato condition on Ricci curvature, uncovering insights on Kato limit spaces and Riemannian manifolds.
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1 Lesons
37 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Unified Synthetic Ricci Curvature Lower Bounds for Riemannian and Sub-Riemannian Geometries

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Explore unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian geometries through gauge metric measure spaces. Discover recent advances in metric measure and sub-Riemannian spaces.
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1 Lesons
45 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Lecture 4

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Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
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1 Lesons
46 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Curvature Tensors and Measures of Singular Spaces - Lecture 3

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Explore advanced concepts in geometry, focusing on curvature tensors and measures of singular spaces in this in-depth mathematical lecture.
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1 Lesons
55 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part II

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Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
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1 Lesons
54 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Geometric Inequalities in Space of Nonpositive Curvature - Part I

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Explore geometric inequalities in spaces of nonpositive curvature, focusing on advanced mathematical concepts and their applications.
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1 Lesons
54 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part I

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Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
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1 Lesons
47 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Curvature Tensors and Measures of Singular Spaces - Part I

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Explore curvature tensors and measures of singular spaces in advanced geometry, focusing on concepts beyond Riemannian geometry.
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1 Lesons
50 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Globally Hyperbolic Anti-de Sitter Manifolds and Compact Clifford-Klein Forms

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Explore globally hyperbolic anti-de Sitter manifolds and compact Clifford-Klein forms in advanced geometry, focusing on curvature and rigidity concepts.
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1 Lesons
50 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A Unified Approach to Extremal Curves on Stiefel Manifolds

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Explore extremal curves on Stiefel manifolds through a unified framework, examining Euler-Lagrange equations and their applications in applied mathematics.
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1 Lesons
49 minutes
On-Demand
Free-Video
NCCR SwissMAP

Marked Length Spectrum Rigidity for Surfaces with Anosov Geodesic Flows

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Explorez les techniques analytiques en dynamique et géométrie, en mettant l'accent sur la rigidité du spectre de longueur marqué pour les surfaces à flux géodésique d'Anosov.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Nash's C^1 Isometric Embedding Theorem and the Borisov-Gromov Problem - Lecture 3

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Explore Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem in Riemannian geometry. Delve into surprising constructions and open questions linked to the Onsager conjecture.
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1 Lesons
1 hour 53 minutes
On-Demand
Free-Video
Conference GSI

Riemannian Geometry of Gibbs Cones Associated to Nilpotent Orbits of Simple Lie Groups

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Explore Riemannian geometry of Gibbs cones linked to nilpotent orbits in simple Lie groups, delving into advanced mathematical concepts and their applications.
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1 Lesons
21 minutes
On-Demand
Free-Video
Conference GSI

Existence of Global Minimizer for Elastic Variational Obstacle Avoidance Problems on Riemannian Manifolds

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Explore global minimizer existence for elastic variational obstacle avoidance problems on Riemannian manifolds. Gain insights into advanced mathematical concepts and their applications.
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1 Lesons
20 minutes
On-Demand
Free-Video
Conference GSI

Using a Riemannian Elastic Metric for Statistical Analysis of Tumor Cell Shape Heterogeneity

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Analyze tumor cell shape heterogeneity using Riemannian elastic metrics for advanced statistical insights in cancer research.
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1 Lesons
20 minutes
On-Demand
Free-Video
Conference GSI

Fisher Rao Riemannian Geometry of Equivalent Gaussian Measures on Hilbert Space

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Explore Fisher Rao Riemannian geometry of equivalent Gaussian measures in Hilbert space, delving into advanced mathematical concepts and their applications.
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1 Lesons
24 minutes
On-Demand
Free-Video
Conference GSI

Rethinking the Riemannian Logarithm on Flag Manifolds as an Orthogonal Alignment Problem

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Explore the Riemannian logarithm on flag manifolds through the lens of orthogonal alignment, offering a fresh perspective on this complex mathematical concept.
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1 Lesons
23 minutes
On-Demand
Free-Video
Conference GSI

Towards Quotient Barycentric Subspaces

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Explore advanced mathematical concepts of quotient barycentric subspaces, delving into their properties and applications in geometric data analysis.
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1 Lesons
22 minutes
On-Demand
Free-Video
Conference GSI

Geodesic Flows of Alpha Connections for Statistical Transformation Models on Compact Lie Groups

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Explore geodesic flows of α connections in statistical transformation models on compact Lie groups, advancing understanding of geometric structures in statistics.
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1 Lesons
22 minutes
On-Demand
Free-Video
Conference GSI

Conformal Submersion with Horizontal Distribution and Geodesics

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Explore conformal submersion, horizontal distribution, and geodesics in differential geometry, enhancing understanding of these advanced mathematical concepts.
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1 Lesons
21 minutes
On-Demand
Free-Video
Conference GSI

On the Tangent Bundles of Statistical Manifolds

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Explore tangent bundles of statistical manifolds, delving into advanced concepts in differential geometry and information geometry.
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1 Lesons
24 minutes
On-Demand
Free-Video
Conference GSI

Three Methods to Put a Riemannian Metric on Shape Space

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Explore three approaches for applying Riemannian metrics to Shape Space, enhancing understanding of geometric analysis in shape theory.
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1 Lesons
28 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Levi-Civita Connection, Christoffel Symbols, and Geodesics - Lecture 7

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Explore advanced concepts in differential geometry, including Levi-Civita connections, Christoffel symbols, and geodesics. Delve into covariant derivatives, parallel transport, and variational principles in this graduate-level lecture.
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11 Lesons
1 hour 43 minutes
On-Demand
Free-Video
NCCR SwissMAP

Nijenhuis Geometry Symmetries, Conservation Laws and Applications to Geodesically Equivalent Metrics

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Explore Nijenhuis Geometry symmetries, conservation laws, and their applications to geodesically equivalent metrics. Gain insights from A. Bolsinov's expert perspective.
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1 Lesons
55 minutes
On-Demand
Free-Video
NCCR SwissMAP

Closed Geodesics and Intersection Numbers in Dynamics and Geometry

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Explorez les techniques analytiques en dynamique et géométrie, en mettant l'accent sur les géodésiques fermées et les nombres d'intersection.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Spherical Plateau Problem and Applications in Geometric Analysis

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Explore area minimization in Hilbert sphere quotients, entropy inequality, and stability results for Riemannian surfaces, with applications to hyperbolic geometry and eigenvalue bounds.
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14 Lesons
1 hour
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Scalar Curvature Rigidity in Manifolds

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Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.
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1 Lesons
48 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Scalar Curvature Rigidity and Extremality in Dimension 4

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Explore scalar curvature rigidity in 4D using Finsler-Thorpe trick and twisted spinor methods. Discover area-extremal properties of 4-manifolds with nonnegative sectional curvature.
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1 Lesons
46 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Intrinsic Flat Stability of the Positive Mass Theorem for Graphical Manifolds

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Explore intrinsic flat stability of positive mass theorem for graphical manifolds, focusing on asymptotically flat and hyperbolic cases. Gain insights into rigidity, stability, and ongoing research.
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1 Lesons
53 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Area-Minimizing Integral Currents: Singularities and Structure - Lecture

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Explore area-minimizing integral currents, their singularities, and structure. Delve into dimension bounds, fractal properties, and recent progress towards proving key conjectures in geometric measure theory.
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10 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Divisible Convex Sets with Properly Embedded Cones

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Explore divisible convex sets, their theory, and new examples in projective geometry. Delve into connections with dynamical systems, geometric group theory, and Riemannian geometry.
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9 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Uniform Volume Doubling and Functional Inequalities on Lie Groups

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Explore functional inequalities on Lie groups, focusing on uniform volume doubling and its implications for SU(2) and related structures. Gain insights into heat kernel estimates and measure contracting properties.
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1 Lesons
58 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

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Explore the interaction between hyperbolic geometry and homology cobordism in low-dimensional topology using monopole Floer homology to study subgroups of the homology cobordism group.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Conjugate Points and the MC Criterion in Volume-Preserving Diffeomorphisms - Lecture

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Explore conjugate points on volume-preserving diffeomorphisms, focusing on the MC criterion and its applications in fluid dynamics and Riemannian geometry.
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10 Lesons
44 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Comparing Oresme's Curvitas with Riemann's Curvature

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Explore the historical evolution of curvature concepts from Oresme's 14th-century insights to Riemann's geometric definitions, examining their mathematical and philosophical implications.
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1 Lesons
1 hour 55 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Width, Scalar Curvature and Macroscopic Scalar Curvature

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Explore the interplay between positive scalar curvature and macroscopic scalar curvature, examining Urysohn width and closed geodesics in PSC and PMSC spaces.
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1 Lesons
39 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Spectra of Laplace and Dirac Operators on Noncompact Manifolds

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Explore spectra of Laplace and Dirac operators on complete manifolds, including types of spectra, results for special behaviors at infinity, and effects of additional potentials.
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1 Lesons
46 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Another Aspect of Gromov's Conjectures on Scalar Curvature

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Explore Gromov's scalar curvature conjectures through general relativity, examining partial solutions via the positive mass theorem.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Geometric Variational Methods for Scalar Curvature and Other Curvature Problems

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Explore geometric variational problems and their applications to curvature conditions, focusing on Schoen-Yau's approach and recent extensions.
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1 Lesons
49 minutes
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Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Stability of Llarull's Theorem in All Dimensions

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Explore stability of Llarull's theorem in all dimensions using spin geometry, with results in intrinsic flat and C^0-convergence outside small sets.
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1 Lesons
52 minutes
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Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Global Effects of Positive Scalar Curvature in Geometry

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Explorez les effets globaux de la courbure scalaire positive, y compris le problème de remplissage de Gromov et les théorèmes de type Llarull sur les variétés complètes.
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1 Lesons
44 minutes
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Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Positive Mass Theorem and Positive Scalar Curvature with Singularities

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Explore recent developments in positive mass theorem and scalar curvature, focusing on singular metrics and isolated conical singularities in mathematical physics.
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1 Lesons
48 minutes
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Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Positive Scalar Curvature with Point Singularities

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Explore topological construction of positive scalar curvature metrics with Euclidean point singularities, challenging Schoen's conjecture and geometric flow limitations.
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1 Lesons
1 hour 21 minutes
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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
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Centre de recherches mathématiques - CRM

Linear Programming Bounds for Hyperbolic Surfaces - Seminar on Spectral Geometry

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Explore linear programming bounds for hyperbolic surfaces, examining closed geodesics and Laplace eigenvalues. Gain insights into quantitative behavior and predominance in Riemannian metrics.
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1 Lesons
1 hour
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Centre de recherches mathématiques - CRM

Eigenvalues and Minimal Surfaces

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Explore Laplace operator eigenvalues, their physical significance, and connection to minimal surfaces. Discover recent findings in isoperimetric eigenvalue problems for Riemannian surfaces.
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1 Lesons
1 hour 2 minutes
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Free-Video
Centre de recherches mathématiques - CRM

New Minimal Surfaces via Equivariant Eigenvalue Optimization - Part II

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Explore equivariant optimization of Laplace and Steklov eigenvalues on surfaces to construct embedded minimal surfaces in 3-sphere and 3-ball. Discover new insights into geometric analysis and topology.
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1 Lesons
58 minutes
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Free-Video