Manifolds Courses and Certifications

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups

Delve into advanced concepts of hyperbolic geometry, exploring manifolds, smooth structures, and group actions through an expert lecture from Brown University's mathematics department.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Critical Regularity and Subexponential Growth in Homeomorphism Groups of Compact Manifolds

Delve into advanced group theory concepts exploring homeomorphism groups of compact connected manifolds and their elementary equivalence, with applications to Whittaker's theorem and manifold classification.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Polyhedra, Hyperbolic 3-Manifolds, and Arithmetic

Explore the connection between polyhedra, hyperbolic 3-manifolds, and arithmetic in this mathematical lecture examining Thurston's construction and the question of arithmeticity.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Using Logic to Investigate Homeomorphism Groups of Manifolds

Delve into the application of logic and descriptive set theory to understand countable groups acting on manifolds, extending beyond classical characterizations of homeomorphism groups.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

The Julia Programming Language

Manifolds in Numerical Computations with JuliaManifolds

Explore JuliaManifolds for robotics, optimization, and statistical tools on manifolds, covering geometric Kalman filters, Manopt.jl performance, and advanced manifold-based models.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

SUSY Compactifications and Arithmetic of Calabi-Yau Manifolds

Explore SUSY compactifications and arithmetic properties of Calabi-Yau manifolds in this advanced mathematical presentation by Mohamed Elmi from YMSC, China.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

INI Seminar Room 2

Spectral Inequalities for the Laplacian on Manifolds with Bounded Sectional Curvature

Explore spectral inequalities for the Laplacian on manifolds with bounded sectional curvature through advanced mathematical analysis and geometric spectral theory applications.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

The Bright Side of Mathematics

Manifolds

Explore key concepts in topology and geometry, including Hausdorff spaces, quotient spaces, and smooth structures, to gain a comprehensive understanding of manifolds.

• YouTube
• 2 hours 30 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Análise em Variedades (2024)

Explore variedades diferenciáveis, formas diferenciais, Teorema de Stokes e cohomologia de De Rham neste programa avançado de matemática do IMPA com Professor Vinicius Ramos.

• YouTube
• 1 day 15 hours 10 minutes
• On-Demand
• Free Video

ICTP Mathematics

Four-Manifolds with Boundary and Fundamental Group Z

Explore advanced concepts in geometry and topology, focusing on four-manifolds with boundary and fundamental group Z, presented by MIT expert Lisa Piccirillo.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Insights into Mathematics

Classification of 2-Manifolds and Euler Characteristic - Differential Geometry

Explore the classification of compact, oriented 2-manifolds and their Euler characteristics through combinatorial methods, cut-and-paste operations, and topological invariants in differential geometry.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Steve Brunton

Topics in Dynamical Systems - Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos

Explore dynamical systems: fixed points, linearization, manifolds, bifurcations, and chaos. Gain insights into nonlinear dynamics and their applications in describing our changing world.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Geometry for Higher Spin Gravity - Conformal Structures, PDEs, and Q-manifolds

Explore advanced mathematical frameworks connecting higher-spin gravity, conformal geometry, and quantum field theory through expert lectures on Cartan geometries, holography, and PDEs.

• YouTube
• 2 days 15 hours 48 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups (2025)

Explore cutting-edge developments in hyperbolic geometry and group theory through expert lectures and hands-on minicourses from leading mathematicians worldwide.

• YouTube
• 1 day 6 hours 39 minutes
• On-Demand
• Free Video

NPTEL;  IISc Bangalore

An Introduction to Smooth Manifolds

The course will start with a brief outline of the prerequisites from topology and multi-variable calculus. After that a large class of examples, including Lie groups, will be presented. The course will culminate with proof of Stokes' theorem on manifolds.

• YouTube
• 1 day 11 hours
• On-Demand
• Free Video