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Insights into Mathematics

Classical Spherical Trigonometry - Universal Hyperbolic Geometry

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Comprehensive overview of classical spherical trigonometry, covering key concepts, laws, and theorems. Introduces a new algebraic approach to simplify and enhance the traditional framework.
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9 Lesons
35 minutes
On-Demand
Free-Video
Institute for Advanced Study

Non-escape of Mass for Arithmetic Quantum Limits on Hyperbolic 4-Manifolds

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Explore the intricacies of the Arithmetic Quantum Unique Ergodicity (AQUE) conjecture in this advanced mathematics seminar. Delve into the groundbreaking research on non-escape of mass for Hecke-Maass cusp forms on congruence quotients of hyperbolic 4-sp…
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Institute for Advanced Study

Non-escape of Mass for Arithmetic Quantum Limits on Hyperbolic 4-Manifolds

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Explore non-escape of mass for Hecke-Maass cusp forms on hyperbolic 4-manifolds, addressing challenges in unbounded Hecke relations and utilizing quaternionic matrices for unique factorization.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Association for Computing Machinery (ACM)

MetaHKG: Meta Hyperbolic Learning for Few-shot Temporal Reasoning - M1.2

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Explore meta hyperbolic learning for few-shot temporal reasoning in knowledge graphs, enhancing reasoning capabilities with limited data.
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1 Lesons
13 minutes
On-Demand
Free-Video

Cool Math Series

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Explore fascinating mathematical concepts, from knot theory to non-Euclidean geometry, in an accessible and engaging series designed for a wide audience.
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23 Lesons
4 hours 30 minutes
On-Demand
Free-Video
Institute for Advanced Study

Raytracing and Raymarching Simulations of Non-Euclidean Geometries - Henry Segerman

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Explore advanced raytracing and raymarching techniques for simulating non-Euclidean geometries, covering fractal objects, isometries, and complex mathematical concepts.
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22 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Floating Bodies and Duality in Spaces of Constant Curvature

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Explores p-affine surface area and floating bodies in curved spaces, extending Meyer & Werner's Euclidean results to spherical and hyperbolic geometries. Examines limiting behavior as curvature approaches zero.
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1 Lesons
30 minutes
On-Demand
Free-Video
ICTP-SAIFR

Anti de Sitter - Class 2

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Explore Anti de Sitter space in theoretical physics with Pedro Vieira, delving into advanced concepts and applications in this comprehensive lecture.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Plongements du Disque de Poincaré dans l'Espace Ambiant - Partie III

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Découvrez la construction explicite d'un plongement isométrique C^1 du disque de Poincaré, explorant ses propriétés surprenantes et son importance en géométrie hyperbolique.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Plongements du Disque de Poincaré dans l'Espace Ambiant - Partie I

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Découvrez la construction explicite d'un plongement isométrique C^1 du disque de Poincaré, explorant ses propriétés surprenantes et son importance en géométrie hyperbolique.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Plongements du Disque de Poincaré dans l'Espace Ambiant - Partie II

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Explorez la construction explicite d'un plongement isométrique C^1 du disque de Poincaré, découvrant ses propriétés surprenantes et son importance en géométrie hyperbolique.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Les mondes mathématiques de Maryam Mirzakhani - Espaces de formes

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Explorez les contributions révolutionnaires de Maryam Mirzakhani aux espaces de formes et à la géométrie, présentées par Pascal Hubert.
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1 Lesons
35 minutes
On-Demand
Free-Video
Open Data Science

From Hyperbolic Geometry to Data Clustering

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Explore how hyperbolic geometry and knot theory inspire innovative data clustering algorithms, bridging abstract mathematics with practical data science applications.
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18 Lesons
39 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Anti-holomorphic Dynamical Systems on a Torus - Applications to Weierstrass Functions

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Explore complex dynamics through anti-holomorphic systems on a torus, examining Weierstrass zeta-functions and their applications to Green functions and constant curvature metrics.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Ergodicity and Horocycle Ergodic Averages on Compact Spaces - Lecture 2

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Delve into ergodic and mixing properties of horocycle flows, exploring their time-changes, asymptotics, and fundamental mathematical concepts in dynamical systems theory.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

On the Dani Correspondence and Its Applications - Lecture 2

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Delve into Diophantine approximation through ergodic theory, exploring the Dani correspondence and its dynamic interpretation of rational number density in the real line.
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9 Lesons
1 hour 1 minute
On-Demand
Free-Video
Simons Semester on Dynamics

Ergodic and Mixing Properties of Horocycle Flows - Lecture 1

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Delve into the mathematical foundations of horocycle flows and their time-changes, exploring ergodic theory, mixing properties, and applications in hyperbolic geometry through advanced theoretical concepts.
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10 Lesons
1 hour
On-Demand
Free-Video
Simons Semester on Dynamics

Time-Changes: Definitions, Basic Facts, Ergodicity and Mixing - Lecture 4

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Delve into ergodic and mixing properties of horocycle flows, exploring time-changes, their parabolic behavior, and fascinating phenomena in dynamical systems and mathematical physics.
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1 Lesons
58 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Mixing and Equidistribution in Horocycle Flows - Lecture 3

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Delve into ergodic theory and mixing properties of horocycle flows, exploring their smooth time-changes, rigidity theorems, and applications beyond SL2(R) in dynamical systems.
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13 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Beyond SL2(R): Time-Changes and Other Perturbations in Different Settings - Lecture 6

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Delve into advanced mathematical concepts of horocycle flows, exploring their ergodic properties, mixing phenomena, and applications beyond SL2(R) in dynamical systems theory.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Rigidity and Ratner's Rigidity Theorem in Horocycle Flows - Lecture 5

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Delve into the rigidity theory of horocycle flows, exploring Ratner's Rigidity Theorem and its implications for dynamical systems in hyperbolic geometry and ergodic theory.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Insights into Mathematics

A Brief History of Geometry III - The 19th Century - Sociology and Pure Mathematics

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Explore the golden age of geometry in the 19th century, covering inversive, projective, non-Euclidean, and complex geometries. Understand key developments and their impact on modern mathematics.
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7 Lesons
53 minutes
On-Demand
Free-Video
Insights into Mathematics

The Classification of Platonic Solids I - Universal Hyperbolic Geometry

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Exploring the classification of Platonic solids using modern notation and turn angles. Examines planar, spherical, and higher-dimensional cases, highlighting mathematical constructions and challenges in Euclid's proof.
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7 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

Petrie Polygons of a Polyhedron - Universal Hyperbolic Geometry

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Explore Petrie polygons on polyhedra, focusing on Platonic solids. Learn about tesselations, Schlafli symbols, and orthogonal projections in this geometric journey.
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7 Lesons
26 minutes
On-Demand
Free-Video
Insights into Mathematics

The Remarkable Platonic Solids I - Universal Hyperbolic Geometry

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Explore the fascinating world of Platonic solids, their symmetry, history, and mathematical properties. Learn about Euclid's contributions and Euler's fundamental relation for polyhedra.
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9 Lesons
26 minutes
On-Demand
Free-Video
Insights into Mathematics

Trigonometric Dual Laws and the Parallax Formula - Universal Hyperbolic Geometry

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Explore trigonometric dual laws and the Right parallax formula in Universal Hyperbolic Geometry. Learn about Pythagoras' theorem, Cross dual law, and zero quadrance/spread theorems.
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7 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Hyperbolic Geometry Is Projective Relativistic Geometry - Full Lecture

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Explore hyperbolic geometry as projective relativistic geometry, covering key concepts, models, and theorems. Gain insights into quadrance, spread, trigonometry, and unique results like the Jumping Jack theorem.
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13 Lesons
51 minutes
On-Demand
Free-Video
Insights into Mathematics

Triangle Geometry Old and New - An Introduction to Hyperbolic Triangle Geometry

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Explore classical and hyperbolic triangle geometry, covering perpendicularity, midpoints, and bilines. Learn about orthocenters, incenters, circumcenters, and more through visual illustrations without complex formulas.
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39 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Insights into Mathematics

Menelaus, Ceva and the Laws of Proportion - Universal Hyperbolic Geometry

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Explore classical theorems of Menelaus and Ceva in universal hyperbolic geometry, along with new results on triangle proportions and alternate spreads. Learn about ratios, distances, and quadrances in triangular geometry.
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8 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

Isosceles Triangles in Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger

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Explore isosceles triangles in hyperbolic geometry, including special formulas, midpoint construction, and related theorems. Gain insights through proofs, exercises, and applications of the cross law.
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9 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

Thales' Theorem, Right Triangles + Napier's Rules - Universal Hyperbolic Geometry

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Explores Thales' theorem and Napier's rules in universal hyperbolic geometry, focusing on right triangles. Covers key concepts like quadrea, spreads, and proofs, with practical exercises for deeper understanding.
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11 Lesons
43 minutes
On-Demand
Free-Video
Insights into Mathematics

The Two-Holed Torus and 3-Crosscaps Surface - Algebraic Topology - NJ Wildberger

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Explore hyperbolic geometric structures of two-holed torus and 3-crosscaps surface through tessellations, hexagons, and the Beltrami Poincare model in this advanced algebraic topology lecture.
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8 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

The Cross Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger

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Explores the Cross law in Universal Hyperbolic Geometry, proving it with a polynomial identity and demonstrating its application to equilateral triangles. Includes exercises and comparisons to Euclidean geometry.
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7 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

The Spread Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry

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Explores the Spread law in universal hyperbolic geometry, including its definition, relation to Euclidean geometry, proof, and implications. Covers key concepts like quadrance, spread duality, and quadrea.
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7 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Visualizing Quadrance with Circles - Universal Hyperbolic Geometry - NJ Wildberger

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Explore quadrance in universal hyperbolic geometry through circles, examining their appearance as ellipses, parabolas, or hyperbolas with different centers, enhancing understanding of this fundamental concept.
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6 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

The Triple Quad Formula in Universal Hyperbolic Geometry

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Explores the Triple quad formula in hyperbolic geometry, its proof, and related concepts. Compares with Euclidean geometry and discusses algebraic challenges, providing exercises for deeper understanding.
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9 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Pythagoras' Theorem in Universal Hyperbolic Geometry

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Explore the hyperbolic version of Pythagoras' theorem, its importance in geometry, and the concept of quadrance. Learn about planar coordinates, formulas, and proofs in Universal Hyperbolic Geometry.
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9 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Quadrance and Spread - Universal Hyperbolic Geometry

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Introduces algebraic definitions of quadrance and spread in Universal Hyperbolic Geometry, comparing with Rational Trigonometry and exploring main laws and exercises in this advanced mathematical framework.
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8 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Perpendicularity, Polarity and Duality on a Sphere - Universal Hyperbolic Geometry

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Explore perpendicularity, polarity, and duality on a sphere, including polar triangles and point-plane duality. Gain insights into elliptic geometry and the relationships between geometric elements.
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7 Lesons
32 minutes
On-Demand
Free-Video
Insights into Mathematics

The J Function, SL(2) and the Jacobi Identity - Universal Hyperbolic Geometry

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Explores connections between hyperbolic geometry, matrix algebra, and Lie theory, demonstrating how the Jacobi identity proves the concurrence of triangle altitudes in projective geometry.
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7 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

Parallels and the Double Triangle - Universal Hyperbolic Geometry

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Explores parallels, double triangles, and perspective centers in Universal Hyperbolic Geometry, offering new insights into Euclid's parallel postulate and its historical implications.
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8 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Medians, Midlines, Centroids and Circumcenters - Universal Hyperbolic Geometry

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Explore triangle geometry in universal hyperbolic geometry, covering medians, midlines, centroids, and circumcenters. Discover unique properties and connections in this algebraic framework.
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8 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Reflections and Projective Linear Algebra - Universal Hyperbolic Geometry

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Explore reflections in hyperbolic geometry through projective linear algebra. Learn about null points, reflection matrices, and the sl(2) Lie algebra. Gain insights into fundamental symmetries and their mathematical representations.
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10 Lesons
50 minutes
On-Demand
Free-Video
Insights into Mathematics

Midpoints and Bisectors - Universal Hyperbolic Geometry

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Explore midpoints and bisectors in hyperbolic geometry, including reflections, perpendicularity, and geometric constructions. Learn key differences from Euclidean geometry in this advanced mathematical exploration.
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11 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

Non-Euclidean Geometry - Math History - NJ Wildberger

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Explore the complex history and modern interpretations of non-Euclidean geometry, challenging traditional narratives and proposing new perspectives on this fundamental mathematical concept.
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8 Lesons
51 minutes
On-Demand
Free-Video
Insights into Mathematics

Apollonius and Polarity Revisited - Universal Hyperbolic Geometry

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Explores Apollonius' polarity in hyperbolic geometry, focusing on null points, quadrangles, and the relationship between poles and polars. Includes explicit formulas and computational examples.
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8 Lesons
27 minutes
On-Demand
Free-Video
Insights into Mathematics

Theorems Using Perpendicularity - Universal Hyperbolic Geometry

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Explore perpendicularity in hyperbolic geometry, including duality, triangles, and the Base center point. Learn a general theorem approach and investigate concepts using Standard Triangle 1.
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8 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

Orthocenters Exist - Universal Hyperbolic Geometry

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Explores orthocenters in universal hyperbolic geometry, introducing key concepts like triangles, altitudes, and Desargues' theorem. Culminates in defining orthic line, orthostar, and ortho-axis in hyperbolic triangle geometry.
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10 Lesons
44 minutes
On-Demand
Free-Video
Insights into Mathematics

Duality and Perpendicularity - Universal Hyperbolic Geometry

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Explore perpendicularity in universal hyperbolic geometry, including duality, altitudes, and key theorems. Learn about unique aspects like perpendicular points and their applications in geometric analysis.
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9 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

Computations with Homogeneous Coordinates - Universal Hyperbolic Geometry

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Explore algebraic definitions of points and lines in hyperbolic geometry, learn key theorems, and understand their applications in computational geometry and Cartesian coordinates.
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9 Lesons
45 minutes
On-Demand
Free-Video
Insights into Mathematics

First Steps in Hyperbolic Geometry - Universal Hyperbolic Geometry

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Explore fundamental concepts of universal hyperbolic geometry, including perpendicularity, quadrance, spread, and key theorems, with a focus on projective study of circles and relativistic geometry.
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9 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

Apollonius and Harmonic Conjugates - Universal Hyperbolic Geometry 2 - NJ Wildberger

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Explore harmonic conjugates in geometry, including their relation to circles, conics, and quadrangles. Learn about harmonic ranges, pencils, and vector combinations in this advanced mathematical discussion.
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7 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

Apollonius and Polarity - Universal Hyperbolic Geometry

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Explore Apollonius' polarity concept in hyperbolic geometry, focusing on the crucial role of circles and their relationship to points and lines in the projective plane.
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8 Lesons
41 minutes
On-Demand
Free-Video
Insights into Mathematics

Universal Hyperbolic Geometry - NJ Wildberger

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Discover a revolutionary approach to hyperbolic geometry, simplifying complex concepts using high school algebra and projective geometry, with connections to Einstein's special relativity theory.
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9 Lesons
23 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
Hausdorff Center for Mathematics

Percolation on Hyperbolic Poisson-Voronoi Tessellations

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Explore percolation on hyperbolic Poisson-Voronoi tessellations, resolving conjectures about critical probability behavior and its dependence on Poisson process intensity.
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15 Lesons
32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Hyperbolic Geometry, the Modular Group and Diophantine Approximation - Lecture 1

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Explore hyperbolic geometry, modular groups, and Diophantine approximation in this advanced lecture. Delve into fundamental concepts, geodesic flows, and subgroups of SL(2,R), with proofs and examples.
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20 Lesons
1 hour 14 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Hyperbolic Surfaces and Their Teichmüller Spaces - Lecture 2

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Explore hyperbolic surfaces, Teichmüller spaces, and surface group representations. Delve into geometric structures, developing maps, and holonomy representations in this advanced mathematics lecture.
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28 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Fields Institute

Donald Coxeter and Geometry

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Explore Donald Coxeter's contributions to geometry, including non-Euclidean geometries, higher dimensions, and connections to art and music in this engaging mathematical journey.
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11 Lesons
55 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
IMSA

Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

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Explore the interaction between hyperbolic geometry and homology cobordism using monopole Floer homology, focusing on subgroups generated by hyperbolic homology spheres.
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1 Lesons
52 minutes
On-Demand
Free-Video
International Mathematical Union

Groups Acting on Hyperbolic Spaces - A Survey

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Explore group actions on hyperbolic spaces with Mladen Bestvina in this comprehensive survey, covering key concepts, recent developments, and applications in geometric group theory.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Some Comments on the Fundamental Gap of the Dirichlet Laplacian in Hyperbolic Space

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Explore the fundamental gap of convex domains in hyperbolic space, comparing it with Euclidean space and examining different types of convexity in this advanced mathematical analysis.
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1 Lesons
40 minutes
On-Demand
Free-Video
QuantumTopology

On Volumes of Compact and Non-Compact Right-Angled Hyperbolic Polyhedra

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Explore the mathematical intricacies of right-angled hyperbolic polyhedra, examining volume calculations for both compact and non-compact forms in this advanced geometry lecture.
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1 Lesons
50 minutes
On-Demand
Free-Video
QuantumTopology

A. Gaifullin - Analytic Continuation of the Volume of Hyperbolic Tetrahedron

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Explore the mathematical concept of analytic continuation applied to hyperbolic tetrahedron volumes, delving into advanced geometric and topological theories.
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1 Lesons
1 hour 24 minutes
On-Demand
Free-Video
APS Physics

Inverse Problems on Graphs with Geometric Deep Learning

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Explores geometric deep learning for graph inverse problems, focusing on non-Euclidean geometries, physics-based approaches, and applications in particle physics and community detection.
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21 Lesons
33 minutes
On-Demand
Free-Video
The Royal Institution

How Geometry Created Modern Physics

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Explore the evolution of geometry from Euclid to Einstein, uncovering how post-Euclidean concepts revolutionized our understanding of spacetime and laid the foundation for modern physics.
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24 Lesons
1 hour 2 minutes
On-Demand
Free-Video
The Royal Institution

The Story of Mathematical Proof - From Ancient Greece to Modern Logic

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Explore the evolution of mathematical proof across number theory, geometry, topology, and logic, delving into the fascinating gap between natural and real numbers.
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18 Lesons
44 minutes
On-Demand
Free-Video
physicsteachers

Of Corals and the Cosmos - A Story of Hyperbolic Space

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Explore hyperbolic geometry in nature, from corals to cactuses, and its historical significance. Discover how these forms challenge traditional Euclidean concepts and their prevalence in the natural world.
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1 Lesons
52 minutes
On-Demand
Free-Video
Insights into Mathematics

Null Points and Null Lines in Universal Hyperbolic Geometry - Lecture 12

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Explore null points and null lines in universal hyperbolic geometry, including rational and projective parametrization, joins and meets theorems, and a triply nil triangle.
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7 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

The Circle and Projective Homogeneous Coordinates - Universal Hyperbolic Geometry Lecture 7a

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Introduction to projective geometry and its relation to universal hyperbolic geometry, exploring concepts like affine spaces, perspective, and one-dimensional projective geometry.
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1 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

The Circle and Projective Homogeneous Coordinates in Universal Hyperbolic Geometry - Lecture 7b

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Explores projective geometry as the foundation of universal hyperbolic geometry, focusing on the circle in projective homogeneous coordinates and its significance in mathematics and physics.
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1 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

The Circle and Cartesian Coordinates in Universal Hyperbolic Geometry - Lecture 5

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Explore Cartesian coordinates and the unit circle, covering key theorems on lines, points, and circles. Learn about determinants, parametrization, and the intersection of lines and circles in geometry.
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7 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Pappus' Theorem and Cross Ratio in Projective Geometry - Universal Hyperbolic Geometry 3

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Explore Pappus' theorem, cross ratio, and key projective geometry concepts. Learn about invariance, transformations, and applications in hyperbolic geometry through theorems and exercises.
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10 Lesons
22 minutes
On-Demand
Free-Video
Insights into Mathematics

The Geometry of Surfaces - Algebraic Topology Lecture 20

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Explore the connection between 2D surfaces and classical geometries, focusing on isometries and introducing hyperbolic geometry through circle inversions in the Beltrami Poincare disk model.
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1 Lesons
44 minutes
On-Demand
Free-Video
Insights into Mathematics

Trigonometric Laws in Hyperbolic Geometry Using Geometer's Sketchpad - Universal Hyperbolic Geometry 26

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Explore trigonometric laws in hyperbolic geometry using Geometer's Sketchpad. Learn about Pythagoras' theorem, Triple quad formula, Spread law, and Cross law with practical examples and custom tools.
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1 Lesons
20 minutes
On-Demand
Free-Video
Insights into Mathematics

Geometer's Sketchpad and Circles in Universal Hyperbolic Geometry - Lecture 25

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Explore Geometer's Sketchpad for dynamic illustrations in universal hyperbolic geometry. Learn custom tools, construct point duals, and discover various circles, including equidistant curves, in hyperbolic space.
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1 Lesons
25 minutes
On-Demand
Free-Video
Insights into Mathematics

Reflections in Hyperbolic Geometry - Universal Hyperbolic Geometry Lecture 14

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Explore reflections in hyperbolic geometry, comparing with Euclidean counterparts. Discover unique properties and surprising connections to circle geometry in this advanced mathematical exploration.
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8 Lesons
31 minutes
On-Demand
Free-Video
Insights into Mathematics

Applications of Rational Spherical Trigonometry - Universal Hyperbolic Geometry Lecture 43

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Exploring rational spherical trigonometry through a specific spherical triangle example, demonstrating its connection to hyperbolic geometry and three-dimensional space.
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1 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Relativistic Velocity and Core Circles in Rational Geometry - Lecture 4

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Exploring relativistic velocity and core circles in rational geometry, extending Paul Miller's protractor concept to projective quadrance and comparing Euclidean and relativistic geometries.
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6 Lesons
49 minutes
On-Demand
Free-Video
Insights into Mathematics

Duality, Polarity and Projective Linear Algebra - Differential Geometry Lecture 11

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Explores projective geometry, quadratic forms, and pole-polar duality in relation to the unit circle. Connects these concepts to Lorentz/Einstein/Minkowski geometry and Apollonius' work.
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1 Lesons
48 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Probabilistic Methods in Hyperbolic Geometry

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Explore probabilistic approaches to solve geometric and topological questions in hyperbolic manifolds, bridging mathematics domains through innovative analytical techniques.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Dimers and M-curves: Limit Shapes from Riemann Surfaces

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Explore dimer models, M-curves, and limit shapes through algebraic geometry, integrating Riemann surfaces and Schottky uniformization. Gain insights into statistical mechanics and discrete geometry.
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1 Lesons
53 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Geometric Bounds for Spanning Tree Entropy of Planar Lattices

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Explores geometric bounds for spanning tree entropy in planar lattices, connecting hyperbolic geometry, number theory, probability, and graph theory. Discusses conjectures and recent progress.
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1 Lesons
43 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
IMSA

Higgs Bundles, Convex Cocompact Subgroups of SU(1,n), and Slodowy Slices

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Explore Higgs bundles, SU(1,n) subgroups, and Slodowy slices. Discover connections between stable Higgs bundles and holonomy groups, focusing on SU(1,n) representations and complex hyperbolic manifolds.
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1 Lesons
1 hour 8 minutes
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Free-Video
International Centre for Theoretical Sciences

Stationary Measures for Fuchsian Groups and Related Contexts

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Explore stationary measures for Fuchsian groups and related contexts, delving into geometric group theory's recent breakthroughs and connections to diverse mathematical areas.
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1 Lesons
46 minutes
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Free-Video
International Centre for Theoretical Sciences

On the Geometry of Extensions of Free Groups

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Explore geometric group theory's advancements, focusing on free group extensions. Gain insights from experts through minicourses and collaborative research in this intensive workshop.
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1 Lesons
49 minutes
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Free-Video
International Centre for Theoretical Sciences

Hyperbolicity - Exploring Negative Curvature in Geometry

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Explore negative curvature and hyperbolicity in everyday objects, from underwater environments to clothing and brain structures, challenging traditional geometry concepts.
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1 Lesons
1 hour 9 minutes
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Free-Video
International Centre for Theoretical Sciences

Anosov Representations and Proper Affine Actions

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Explore Anosov representations and proper affine actions in geometric group theory. Gain insights from expert Sourav Ghosh on this advanced mathematical topic.
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1 Lesons
44 minutes
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Free-Video
TEDx

Negatively Curved Crystals - Exploring Infinite Patterns

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Explore the fascinating world of negatively curved crystals and their infinite patterns with Fields Medal winner Curtis McMullen in this engaging TEDx talk.
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1 Lesons
14 minutes
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Free-Video
Michael Penn

The Strangest Circle - Mathematical Curiosities and Paradoxes

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Explore a fascinating mathematical concept: a circle with peculiar properties that challenge conventional geometry, offering unique insights into advanced mathematical thinking.
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1 Lesons
31 minutes
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Free-Video
Fields Institute

Dynamical Systems Arising from the Classification of Geometric Structures

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Explore dynamical systems in geometric structure classification, delving into mathematical concepts and their applications in topology and geometry.
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1 Lesons
56 minutes
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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
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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
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The Funk Metric in Convex Geometry and Related Fields

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Explore the Funk metric's connections to convex geometry, affine geometry, and combinatorics. Discover its projective invariance and relations to various conjectures and theorems.
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1 Lesons
53 minutes
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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
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Free-Video
Centre International de Rencontres Mathématiques

Hyperbolic Voronoi Percolation

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Explore hyperbolic Voronoi percolation in this mathematical conference talk. Gain insights into non-Euclidean geometry and probability theory from expert Tobias Müller.
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1 Lesons
50 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
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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
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