Hyperbolic Geometry Courses and Certifications

The Geometry of Möbius Transformations

Explore the elegant geometry of Möbius transformations, uncovering their role as fundamental symmetries of the Riemann sphere, bridging complex analysis, geometry, and mathematical physics.

• Swayam
• Self-Paced
• Free Online Course

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.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

TED

The Beautiful Math of Coral and Crochet

Explore the fascinating intersection of mathematics, marine biology, and crochet as Margaret Wertheim recreates coral reef structures, revealing the hyperbolic geometry underlying their intricate forms.

• YouTube
• 17 minutes
• Self-Paced
• Conference Talk

Institut des Hautes Etudes Scientifiques (IHES)

Workshop on Quantum Geometry

Explore advanced quantum geometry through expert lectures on Gromov-Witten theory, Donaldson-Thomas invariants, integrable systems, and spectral curve quantization from leading researchers.

• YouTube
• 14 hours 45 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Mathematical Physics Seminar - Log-Sobolev Inequality, Maass Spectra, Grassmann Integrals, and Advanced Topics

Explore advanced mathematical physics topics including Ising models, Maass spectra, Grassmann integrals, flat surfaces, Gibbs measures, and conformal field theory.

• YouTube
• 8 hours 59 minutes
• Self-Paced
• Free Video

TED-Ed

The Beautiful Math of Coral

Explore the mesmerizing intersection of mathematics and marine biology as Margaret Wertheim recreates coral reef creatures, revealing the hyperbolic geometry underlying their intricate structures.

• YouTube
• 16 minutes
• Self-Paced
• Conference Talk

The Royal Institution

Topology, Geometry and Life in Three Dimensions

Explore hyperbolic geometry's role in mapping complex 3D spaces and its influence on digital art. Learn about mathematical approaches to describing and investigating intricate maze-like structures.

• YouTube
• 58 minutes
• Self-Paced
• Conference Talk

Insights into Mathematics

The Geometry of Surfaces - Algebraic Topology Lecture 20

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.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Mathemaniac

How Physics Solves Plateau's Problem - Applications in Math and 3D Graphics

Explore how physics and mean curvature flow solve Plateau's problem, with applications in mathematics, soap films, and 3D graphics. Discover connections between minimal surfaces and active research areas.

• YouTube
• 18 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Parabolic Dynamics and Renormalization - An Introduction

Explore parabolic dynamical systems and their "slow" chaotic evolution through renormalization techniques, covering linear flows, horocycle flows, nilflows, and area-preserving flows.

• YouTube
• 11 hours 51 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Geometry in Non-Positive Curvature and Kähler Groups

Explore advanced geometric group theory through expert lectures on hyperbolic geometry, Kähler groups, and their interactions in this specialized mathematical conference.

• YouTube
• 10 hours 11 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Frontiers in Geometry and Topology Summer School

Explore advanced topics in geometry and topology including Heegaard Floer homology, Dirac operators, pseudoholomorphic curves, and Seiberg-Witten equations through expert lectures.

• YouTube
• 15 hours 34 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Advanced School on Geometric Group Theory and Low-Dimensional Topology - Recent Connections and Advances

Explore cutting-edge connections between geometric group theory and low-dimensional topology through advanced lectures on virtually special groups, hyperbolic manifolds, and Teichmuller theory.

• YouTube
• 22 hours 54 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Heegaard Floer Homology

Dive into Heegaard Floer homology through comprehensive lectures covering fundamental concepts and advanced applications in low-dimensional topology and knot theory.

• YouTube
• 3 hours 53 minutes
• Self-Paced
• Free Video

Insights into Mathematics

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

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.

• YouTube
• 39 minutes
• Self-Paced
• Free Video