Topology Courses and Certifications

Isaac Newton Institute for Mathematical Sciences

Topology, Representation Theory and Higher Structures - Meet the Organisers

Explore the intersection of topology, representation theory, and higher structures with leading mathematicians. Gain insights into this exciting field's challenges, impacts, and potential applications.

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

Schmid College, Chapman University

Topology in 1930s America - A Tale of Two Camps

Explore the rivalry between point-set and combinatorial topology camps in 1930s America, examining their approaches, key figures, and impact on the mathematical research community.

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

ICTP Condensed Matter and Statistical Physics

Topology and Dynamics of Higher-Order Networks - Lecture 3: Topological Dirac Equation and Discrete Network Geometry

Explore topological Dirac equations and discrete network geometry in higher-order networks. Delve into metric cohomology and its applications in mathematical physics and dynamical systems.

• YouTube
• 2 hours 13 minutes
• On-Demand
• Free Video

ICTP Condensed Matter and Statistical Physics

Topology and Dynamics of Higher-Order Networks - Information Theory of Network Geometry and Gauge Fields - Lecture 4

Explore information theory of network geometry and gauge fields in higher-order networks. Delve into topological signals, discrete topology, and emerging dynamical states in complex systems.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Stony Brook Mathematics

On the Applications of Topology

Explore topological methods for analyzing complex data sets, focusing on persistent homology and mapper, with applications in computer vision, biology, and medicine.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Stony Brook Mathematics

Homotopy Groups of Spheres

Explore continuous maps between spheres, their abelian group structures, and connections to key problems in topology with Zhouli Xu from UC San Diego.

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

Stony Brook Mathematics

On Exotic Embeddings of Submanifolds in 4-Manifolds

Explore exotic embeddings of submanifolds in 4-manifolds, focusing on phenomena that survive stabilizations. Delve into advanced 4-dimensional topology concepts and recent research findings.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Institut Henri Poincaré

The Genus-One Question for Open Book Decomposition in Contact Structures and Anosov Flows

Explore the genus-one question for open book decomposition in 3D contact structures and Anosov flows, examining constructions and partial results.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Lipschitz Constant and Degree of Mappings in Riemannian Manifolds

Explore the relationship between Lipschitz constant and degree of mappings in Riemannian manifolds, focusing on recent developments and clever mapping techniques.

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

Institut des Hautes Etudes Scientifiques (IHES)

Geometric Structures Associated to Anosov Representations

Explore geometric structures linked to Anosov representations, focusing on domains of discontinuity and their quotients as smooth fiber bundles over closed hyperbolic manifolds.

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

Insights into Mathematics

Topological Spaces and Manifolds - Differential Geometry Lecture 24

Explore topological spaces and manifolds through neighborhood systems and open sets. Learn key concepts, solve problems, and understand the foundations of continuous space theory in modern mathematics.

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

Insights into Mathematics

Introduction to Topology in Mathematics History

Explore topology's historical development, from Euler's polyhedron discoveries to Poincaré's insights. Learn about key concepts like Euler characteristic, Riemann surfaces, and surface classification in this mathematical journey.

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

HyperComplex Seminar

On Weak 1-Semiconvexity of Open Sets in Euclidean Spaces

Explore weak 1-semiconvexity in Euclidean spaces, examining its properties, connections to linearly accessible domains, and implications for set disconnectedness in higher dimensions.

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

Wolfram

Mathematical Games - Surfaces - Episode 13

Explore mathematical games and puzzles involving surfaces with Ed Pegg Jr. in this engaging 55-minute episode, delving into fascinating geometric concepts and challenges.

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

University of Chicago Department of Mathematics

The Fundamental Group of Random 3-Manifolds and Other Random Objects

Dive into the fundamental group of random 3-manifolds, exploring probability distributions and their applications to various categories in mathematics.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video