Manifolds Courses and Certifications

Harvard CMSA

The Global Sections of Chiral de Rham Complexes on Compact Calabi-Yau Manifolds

Delve into complex mathematical concepts of chiral de Rham complexes, exploring their global sections on compact Calabi-Yau manifolds through theoretical frameworks and detailed proofs.

• YouTube
• 38 minutes
• Self-Paced
• Free Video

Centre de recherches mathématiques - CRM

Graph Structure of the Nodal Set on Riemannian Manifolds

Explore the geometric analysis of eigenfunction zero sets on Riemannian manifolds, examining connections between graph theory, nodal sets, and critical point estimation in spectral geometry.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Arithmetic Properties - Mini-course 2

Delve into advanced concepts of arithmetic hyperbolic manifolds and totally geodesic submanifolds through expert lectures from Matthew Stover and Mikhail Belolipetsky at IMPA's specialized mathematics conference.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Exotic Negatively Curved Manifolds - Mini-course 3

Delve into advanced concepts of exotic negatively curved manifolds and hyperbolic geometry through expert insights from Brown University's mathematical research and developments.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds and Their Totally Geodesic Submanifolds - Mini-course 2

Delve into advanced concepts of arithmetic hyperbolic manifolds and their totally geodesic submanifolds through expert analysis of recent developments in hyperbolic geometry and group theory.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Building Hyperbolic Manifolds with Coxeter Polytopes - Mini-course 3

Delve into advanced hyperbolic geometry concepts through an exploration of building hyperbolic manifolds with Coxeter polytopes, presented by Oxford mathematician Giovanni Italiano.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Building Hyperbolic Manifolds with Coxeter Polytopes - Mini-course 3

Delve into advanced concepts of building hyperbolic manifolds using Coxeter polytopes through expert guidance on geometric construction methods and theoretical foundations.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Totally Geodesic Submanifolds - Mini-course 2

Delve into advanced concepts of arithmetic hyperbolic manifolds and their totally geodesic submanifolds through expert insights from Temple University's Matthew Stover.

• YouTube
• 1 hour 24 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Exotic Negatively Curved Manifolds - Mini-course 2

Delve into advanced concepts of exotic negatively curved manifolds and hyperbolic geometry through expert insights on recent developments in geometric topology and group theory.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lie Algebras of Diffeomorphism Groups of Non-compact Manifolds - Part 1

Delve into advanced mathematical concepts exploring diffeomorphism groups of non-compact manifolds, focusing on their Lie algebra structures and elastic properties in diffeological spaces.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Connections in Infinite-Dimensional Grassmann Manifolds

Explore operator theoretic methods and covariant derivatives in infinite-dimensional Grassmann manifolds, focusing on conjugated points along geodesics and their mathematical implications.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Banach Manifolds and Integrable Systems - KdV and Toda-Lattice Applications

Explore integrable systems like KdV and Toda-lattice through the lens of Banach manifolds, examining their Poisson and symplectic structures in infinite-dimensional geometry.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Hamiltonian Dynamics on Poisson Manifolds and Symplectic Groupoids

Delve into advanced mathematical concepts exploring Hamiltonian dynamics through symplectic Lie groupoids, covering approximation methods and applications in conservative mechanics and PDEs.

• YouTube
• 42 minutes
• Self-Paced
• Free Video

SCI MUNI

Quantum Flag Manifolds and Noncommutative Geometric Representation Theory

Delve into advanced mathematical concepts exploring quantum flag manifolds and their relationship with noncommutative geometric representation theory in modern mathematics.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

SCI MUNI

Solution of the QC Yamabe Equation on 3-Sasakian Manifolds and the QC Yamabe Problem

Delve into quaternionic contact geometry and explore the solution methods for the qc Yamabe equation, focusing on 3-Sasakian manifolds and their mathematical properties.

• YouTube
• 42 minutes
• Self-Paced
• Free Video