Manifolds Courses and Certifications

International Mathematical Union

Aaron Brown- Lattice Subgroups Acting on Manifolds

Explore lattice subgroups' actions on manifolds, covering definitions, theorems, and Zimmer's conjecture. Gain insights into isometric and projective actions, standard modifications, and ongoing research.

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

Fields Institute

Bordism of Manifolds - Lecture 1

Explore the concept of bordism in manifolds with Stanford's Mohammed Abouzaid, delving into advanced mathematical theories and their applications in topology and geometry.

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

ICTP Mathematics

Invariants of Manifolds From 6 Dimensions

Explore advanced mathematical concepts in gauge theories and differential invariants, focusing on invariants of manifolds in higher dimensions.

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

ICTP Mathematics

Fractional Poincare Inequalities on Manifolds With Finite Total Q-Curvature

Explore fractional Poincare inequalities on manifolds, focusing on finite total Q-curvature. Advanced mathematical concepts for geometry and physics enthusiasts.

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

Institute for Pure & Applied Mathematics (IPAM)

Building Manifolds from Error Correcting Codes - IPAM at UCLA

Explore the intersection of error correcting codes and manifold construction, delving into quantum error correction, topology, and complex mathematical concepts.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

ICTP Mathematics

Invariants of Manifolds from 6 Dimensions

Explore advanced mathematical concepts in gauge theories and differential invariants, focusing on invariants of manifolds from 6 dimensions and their applications in theoretical physics.

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

International Centre for Theoretical Sciences

Quadrature Rules on Manifolds - Designs - Lecture 1

Explore quadrature rules on manifolds and designs in harmonic analysis. Learn about cutting-edge mathematical techniques for solving complex problems in geometry and analysis.

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

BIMSA

Distribution on Achiral Manifolds

Explore distribution of commensurable classes in geometric models, focusing on Sol and hyperbolic 3-manifolds. Delve into related number theory concepts and recent research findings.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Isaac Newton Institute for Mathematical Sciences

Random Rubber Bands: Evolution and Noise on Manifolds - Rothschild Lecture

Explore the evolution of random rubber bands on manifolds, delving into mathematical insights and algebraic structures arising from this intriguing model of noisy geodesic behavior.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

De Rham Algebras of Closed Quasiregularly Elliptic Manifolds are Euclidean

Explore quasiregular mappings and de Rham cohomology in closed manifolds, leading to a homeomorphic classification of certain 4-manifolds.

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

University of Chicago Department of Mathematics

Symmetries of Manifolds - Lecture 3

Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.

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

University of Chicago Department of Mathematics

Symmetries of Manifolds - Lecture 2

Delve into symmetries of manifolds, exploring classical and recent results on spaces of symmetries for simple manifolds like spheres and discs, with insights into emerging conjectural perspectives.

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

University of Chicago Department of Mathematics

Symmetries of Manifolds - Lecture 1

Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.

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

NPTEL-NOC IITM

Mathematical Preliminaries - Calculus on Manifolds 1

Explore smooth functions, curves, vectors as differential operators, tangent spaces, one-forms, cotangent spaces, and rank (p,q) tensors in manifold calculus fundamentals.

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

Harvard CMSA

Kernel Learning on Manifolds

Explore L_2 risk bounds for minimum norm interpolation using trace class elliptic kernels on Riemannian manifolds, revealing spectral cutoff relationships between samples and dimensions.

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