Manifolds Courses and Certifications

Introduction to optimization on smooth manifolds: first order methods

Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).

• edX
• 6 weeks, 5-6 hours a week
• On-Demand
• Free Online Course (Audit)

Special Lecture Series on Numerical Geometry - Tristan Collins

Join Tristan Collins from MIT for a special lecture on Numerical Geometry at the University of Miami. Dive into Calabi-Yau metrics, Fano manifolds, and singular divisors in under an hour.

• YouTube
• 51 minutes
• On-Demand
• Free Online Course

Instantons, Suspension, and Surgery

Dive into Gauge Theory and Low Dimensional Topology with Columbia University's Mike Miller Eismeier in a 1-2 hour session, organized by the University of Miami. Explore instantons, suspension, and surgery.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Online Course

Symmetric Approach to General Relativity - Applications to Exotic Spheres

Explore the symmetric approach to General Relativity and its applications to exotic spheres with Leonardo Cavenaghi from the University of Miami. Less than 1-hour workload.

• YouTube
• 58 minutes
• On-Demand
• Free Online Course

The Bright Side of Mathematics

Manifolds

Dive into the world of Manifolds with The Bright Side of Mathematics. Learn about topology, Hausdorff spaces, quotient spaces, and more in this 2-3 hour study.

• YouTube
• 2 hours 30 minutes
• On-Demand
• Free Online Course

Artem Kirsanov

Neural Manifolds - The Geometry of Behaviour

Explore the intersection of neuroscience and topology in this less than 1-hour material by Artem Kirsanov. Gain intuitive understanding of high-dimensional representations in neural circuits.

• YouTube
• 23 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Manifolds, Classification of Surfaces and Euler Characteristic - Differential Geometry

Explore the concept of manifolds, classification of surfaces, and Euler characteristic in this less than 1-hour material by Insights into Mathematics. Delve into charts, orientation, and compact surfaces.

• YouTube
• 46 minutes
• On-Demand
• Free Online Course

Analysis II Video Lectures

Dive into advanced mathematical analysis with 14 hours of video lectures, covering topics from LaTeX and TikZ to integral equations and solutions to ODEs.

• YouTube
• 14 hours
• On-Demand
• Free Online Course

Institute for Pure & Applied Mathematics (IPAM)

Building Manifolds from Error Correcting Codes - IPAM at UCLA

Dive into the mathematics of topological phases of matter with Matthew Hastings of Microsoft Research. This 1-2 hour IPAM program explores error correcting codes and manifold construction.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Invariants of Manifolds from 6 Dimensions

Dive into manifold invariants in 6 dimensions with ICTP Mathematics. Learn from expert Pavel Putrov, exploring topics like schematic fault and generating functions. (1-2 hours)

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Online Course

Yannic Kilcher

Gauge Equivariant Convolutional Networks and the Icosahedral CNN

Explore CNNs over manifolds with Yannic Kilcher's concise study, offering a practical method to achieve top results in various tasks. Ideal for those interested in neural network architecture design.

• YouTube
• 22 minutes
• On-Demand
• Free Online Course

International Mathematical Union

Jennifer Hom: Homology Cobordism and Heegaard Floer Homology

Explore homology cobordism and Heegaard Floer homology in less than an hour with this International Mathematical Union offering. Dive into manifolds, chain complexes, and homomorphisms.

• YouTube
• 44 minutes
• On-Demand
• Free Online Course

International Mathematical Union

Aaron Brown- Lattice Subgroups Acting on Manifolds

Dive into the world of lattice subgroups and manifolds with Aaron Brown's less than 1-hour material from the International Mathematical Union.

• YouTube
• 46 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

Helmut Bölcskei - Lossy Compression on General Data Structures

Explore lossy data compression on general structures, rate-distortion theory, and quantization with the Hausdorff Center for Mathematics. Less than 1-hour workload.

• YouTube
• 44 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Approximate and Discrete Vector Bundles

Explore synchronization problems and dimensionality reduction through principal bundles and local PCA in this 1-2 hour material from Applied Algebraic Topology Network.

• YouTube
• 1 hour
• On-Demand
• Free Online Course