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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
Galileo Galilei Institute

Advanced General Relativity - Lecture 1

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Explore advanced concepts in General Relativity, delving into complex theories and mathematical frameworks that expand upon Einstein's groundbreaking work in spacetime and gravity.
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1 Lesons
2 hours 5 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 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 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 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 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 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
International Centre for Theoretical Sciences

Hyperbolic Geometry, Fuchsian Groups and Moduli Spaces - Lecture 1

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Introducción a la geometría hiperbólica: modelos, propiedades y trigonometría. Exploración de los modelos del semiplano superior, disco y hiperboloide, con énfasis en geodésicas, ángulos y curvatura constante.
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27 Lesons
1 hour 22 minutes
On-Demand
Free-Video
ICTP Mathematics

Some Geometric Properties of Spacetime

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Explore geometric properties of spacetime, including constraint equations, scalar curvature, cone angles, and the positive mass theorem. Gain insights into fundamental concepts in geometry and gravity.
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12 Lesons
1 hour 18 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
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 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
Mathemaniac

Why All Maps Are Wrong - Theorema Egregium

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Explore Theorema Egregium's geometric proof, revealing why no world map can preserve both area and angles. Understand curvature, spherical areas, and the Gauss map in this mathematical journey.
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8 Lesons
40 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
Hausdorff Center for Mathematics

P-adic Height Pairings of Geodesics on Modular Curves

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Explore p-adic height pairings of real quadratic geodesics on modular curves, their relation to real quadratic singular moduli, and insights from triple product period interpretation.
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1 Lesons
1 hour 12 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
Isaac Newton Institute for Mathematical Sciences

Random Rubber Bands: Evolution and Noise on Manifolds - Rothschild Lecture

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Explore the evolution of random rubber bands on manifolds, delving into mathematical insights and algebraic structures arising from this intriguing model of noisy geodesic behavior.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Fields Institute

Riemannian Manifolds, Isometries, and Geodesics - Lecture 3

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Explore Riemannian manifolds, isometries, and geodesics, with a focus on the upper half-plane and hyperbolic metric in this advanced geometry lecture.
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1 Lesons
55 minutes
On-Demand
Free-Video
Conference GSI

The Phase Space Description of the Geodesics on the Statistical Model on a Finite Set - Trajectory

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Explore geodesics on statistical models using phase space descriptions, focusing on finite sets and trajectories in information geometry.
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1 Lesons
21 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
Centrum Fizyki Teoretycznej PAN

Christoffel Symbols, Curvature, and Riemann Tensor - Lecture 8

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Zgłęb zaawansowane koncepcje geometrii różniczkowej, w tym symbole Christoffela, krzywiznę i tensor Riemanna. Poznaj ich właściwości algebraiczne i zastosowania w fizyce teoretycznej.
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12 Lesons
1 hour 47 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

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)

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
Big Ideas In Dynamics

Thurston's Asymmetric Metric on Teichmüller Space Revisited

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Explore Thurston's asymmetric metric on Teichmüller space and its generalizations to higher-rank Lie groups, examining geometric and dynamical invariants of hyperbolic structures.
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1 Lesons
1 hour
On-Demand
Free-Video
International Centre for Theoretical Sciences

Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri by Sunil Mukhi

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Explore advanced topics in General Relativity, including black holes, spacetime geometry, and Raychaudhuri equations. Gain insights into current research and honor the legacy of physicist Amal Kumar Raychaudhuri.
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1 Lesons
1 hour 38 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Riemann Tensor in General Relativity - Lecture 9

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Explore the Riemann tensor through Christoffel symbols, geodesics, 2-sphere geometry, and Rindler spacetime in this advanced graduate-level physics lecture.
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3 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Bogolyubov Institute for Theoretical Physics

Пертурбаційні рівняння для Шварцшильдівської геодезії

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Дослідіть пертурбаційні рівняння для геодезії Шварцшильда та їх застосування в теоретичній фізиці через поглиблений аналіз математичних основ.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Valence Labs

Metric Flow Matching for Smooth Interpolations on the Data Manifold

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Explore Metric Flow Matching for smooth interpolations on data manifolds. Learn about conditional paths, Riemannian metrics, and geodesic interpolants. Discover applications in LiDAR navigation and cellular dynamics modeling.
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8 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Models of Consciousness Conferences

Gnomonic Projection from Objective Flat 3-Space to Subjective Hemi-3-Sphere

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Explores a novel model of visual perception using gnomonic projection to map objective 3D space onto a curved subjective space, explaining phenomena like foreshortening and straight line perception.
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1 Lesons
23 minutes
On-Demand
Free-Video
BIMSA

Understanding the KPZ Problem - A New Perspective on Random Geometry and Universal Statistics

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Delve into the universal properties of random geometries and geodesics in the KPZ framework, exploring statistical mechanics, probability theory, and mathematical physics applications.
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1 Lesons
45 minutes
On-Demand
Free-Video
BIMSA

Rotationally Invariant First Passage Percolation: Scaling Relations and Chaos - ICBS 2024

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Explore rotationally invariant first passage percolation, scaling relations, and chaos in KPZ universality class through multi-scale analysis and geodesic behavior.
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1 Lesons
57 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Elements of General Relativity - Lecture 2

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Explore advanced concepts in general relativity, focusing on geometry beyond Riemann and examining curvature and rigidity in spacetime.
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1 Lesons
55 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Elements of General Relativity - Lecture 3

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Explore advanced concepts in general relativity, focusing on geometry beyond Riemann and examining curvature and rigidity in spacetime.
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1 Lesons
50 minutes
On-Demand
Free-Video
ICTP-SAIFR

Elements of General Relativity and AdS Space

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Explore general relativity and Anti-de Sitter space fundamentals in this introductory minicourse on AdS-CFT, presented by Horatiu Nastase at ICTP-SAIFR.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
BIMSA

Partial Entanglement Network and Geometry Reconstruction in AdS/CFT

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Explore partial entanglement entropy geometrization in AdS/CFT, examining PEE threads, network formation, and bulk geometry reconstruction using novel approaches.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Schwarzschild Metric in General Relativity - Lecture 15

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Explore the Schwarzschild metric's properties, including gravitational effects, geodesics, and orbits in this advanced graduate-level physics lecture on general relativity.
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12 Lesons
1 hour 46 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Schwarzschild Metric and Event Horizon - Lecture 16

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Explore Schwarzschild metric, event horizons, and black hole physics in this graduate-level lecture. Delve into perihelion precession, coordinate systems, and global structure of Schwarzschild solutions.
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10 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Trajectory Inference in Wasserstein Space

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Explore advanced trajectory inference methods using Wasserstein geometry and B-spline approximation for analyzing dynamic processes in computational biology and point cloud data.
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1 Lesons
51 minutes
On-Demand
Free-Video