Differential Topology Courses and Certifications

Hausdorff Center for Mathematics

Differential Topology and First Order Rigidity

Explore how first order theory of diffeomorphism groups determines manifold structure and regularity, strengthening classical results in differential topology.

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

Instituto de Matemática Pura e Aplicada

Elementary Differential Topology Applied to a Problem in Partial Differential Equations: Theoretical Aspects - 2023

Explore elementary differential topology applied to conservation laws, focusing on a 3D wave manifold and its properties for solving Riemann problems in partial differential equations.

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

Institute for Advanced Study

Workshop on the H-Principle and Beyond

Explore advanced mathematical concepts through expert lectures on h-principle theory, differential geometry, fluid dynamics, and symplectic structures in this comprehensive workshop.

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

ICTP Mathematics

Lefschetz Fibrations and Closed Exotic 4-Manifolds - Lecture 1

Explore the mathematical concepts of Lefschetz fibrations and their applications in understanding closed exotic 4-manifolds in this advanced mathematics lecture.

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

ICTP Mathematics

Lefschetz Fibrations and Closed Exotic 4-Manifolds

Explore advanced techniques in 4-dimensional topology through Lefschetz fibrations and their role in constructing exotic smooth structures on closed 4-manifolds.

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

ICTP Mathematics

Lefschetz Fibrations and Closed Exotic 4-Manifolds - 5

Explore advanced techniques in 4-dimensional topology through Lefschetz fibrations and their role in constructing exotic smooth structures on closed 4-manifolds.

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

Centre International de Rencontres Mathématiques

Equivariant Trisections for Group Actions on Four-Manifolds

Explore G-equivariant trisections for 4-dimensional manifolds with group actions, reducing complex topology to 2D shadow diagrams through invariant surface embeddings.

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

BIMSA

Diffeomorphisms of 4-Manifolds

Explore advanced mathematical concepts in 4-dimensional topology through expert analysis of diffeomorphisms and their properties in manifold theory.

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

Simons Institute

On Professor Smale's Legacy for Asymptotic Stability Theory

Explore the topology of asymptotically stable vector fields and Lyapunov functions, connecting Smale's work to differential topology and stability theory applications.

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

Simons Foundation

Smooth Structures on Closed Four-Manifolds with Non-Trivial Fundamental Group - March 27, 2025

Explore key constructions for producing 'exotic' smooth structures on closed four-manifolds with non-trivial fundamental groups, examining sources of exoticness through the genus function on second homology groups.

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

Hausdorff Center for Mathematics

Differential Topology for Diamonds

Explores Banach-Colmez tangent spaces for diamonds in smooth rigid analytic varieties, proposing conjectures on preperfectoid loci and cohomological smoothness, with examples and computations.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Banach Center

Differential Equations and Topology in Algebraic Varieties

Explore differential equations and topology, covering algebraic varieties, De Rham cohomology, monodromy, and the Riemann-Hilbert problem in this advanced mathematical lecture.

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

ICTP-SAIFR

Topology in Partial Differential Equations - Class 3

Delve into analytical and numerical tools for partial differential equations with a focus on topology in this lecture by Oscar Reula from the National University of Córdoba.

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

ICTP-SAIFR

Topology in Partial Differential Equations - Class 4

Delve into analytical and numerical tools for partial differential equations with a focus on topology in this lecture by Oscar Reula from the National University of Córdoba.

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

3Blue1Brown

The Hairy Ball Theorem

Explore the fascinating Hairy Ball Theorem through stunning visual proofs and discover its unexpected applications in topology, vector fields, and mathematical reasoning.

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