Manifolds Courses and Certifications

IMSA

Manifolds and Singular Varieties - Yesterday and Tomorrow

Explore the evolution and future prospects of manifolds and singular varieties theory through foundational research discussions and theoretical developments in mathematics.

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

University of Chicago Department of Mathematics

Theory of Valuations on Manifolds

Explore the concept of valuations on smooth manifolds, including their algebraic structure, relationship to smooth functions and measures, and foundational principles, as introduced by Semyon Alesker.

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

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)

Yannic Kilcher

Gauge Equivariant Convolutional Networks and the Icosahedral CNN

Explore gauge equivariant CNNs on manifolds, focusing on icosahedral surfaces. Learn how this approach improves image segmentation and climate pattern analysis with enhanced efficiency and performance.

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

Artem Kirsanov

Neural Manifolds - The Geometry of Behaviour

Explore the geometry of behavior through neural manifolds, combining topology and neuroscience to understand high-dimensional information in neural circuits. Gain insights into brain function using intuitive explanations.

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

Institut des Hautes Etudes Scientifiques (IHES)

A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Part 1

Explore Gromov's angle shrinking problem and its role in proving the dihedral extremality/rigidity conjecture through a new index theorem for manifolds with polyhedral boundary.

• YouTube
• 52 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

Manifolds, Classification of Surfaces and Euler Characteristic - Differential Geometry

Informal introduction to manifolds, focusing on 2D surfaces. Explores charts, orientation, and classification using Euler characteristic. Highlights key concepts in differential geometry.

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

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups

Delve into advanced hyperbolic geometry concepts through an exploration of manifolds, submanifolds, and fundamental groups, with insights from leading mathematician Monika Kudlinska.

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

Hausdorff Center for Mathematics

Homotopy Theory, Manifolds, and Field Theories

Explore advanced topics in homotopy theory through expert lectures on elliptic cohomology, factorization homology, and moduli spaces of manifolds from leading mathematicians.

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

International Centre for Theoretical Sciences

Quadrature Rules on Manifolds - Useful Results - Lecture 3

Explore advanced quadrature techniques for manifolds, focusing on key results and applications in harmonic analysis. Gain insights into cutting-edge mathematical approaches.

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

BIMSA

Triangulations of Manifolds and the Triangulation Conjecture

Explore the triangulation conjecture in topology, its validity in low dimensions, and its disproval in higher dimensions using advanced mathematical techniques.

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

BIMSA

Positive Scalar Curvature on Manifolds and Foliations - ICBS 2024

Explore recent advances in positive scalar curvature metrics on manifolds and foliations, a key topic in differential geometry.

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

Centre de recherches mathématiques - CRM

Algebraic Presentations of 4- and 3-Manifolds in Low-Dimensional Topology

Explore algebraic presentations of 4- and 3-manifolds, focusing on categories of n-cobordisms and their relation to low-dimensional topology and combinatorial group theory.

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

Institut des Hautes Etudes Scientifiques (IHES)

Regularising Manifolds Using Ricci Flow

Explore Ricci flow's applications in deforming and regularizing manifolds, including its use in identifying topology and proving geometric theorems.

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