Complex Geometry Courses and Certifications

The Royal Institution

The Search for a Theory of Everything – with Yang-Hui He

Explore the quest for a unified theory of everything, tracing its history from ancient astronomers to modern string theory and the interplay between physics, mathematics, and data.

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

Hackaday

Designing with Complex Geometry - Class 4

Explore advanced Grasshopper techniques including L-Systems, attractor points, vector lines, and fields. Learn to create complex geometries and enhance your parametric design skills.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Hackaday

Designing with Complex Geometry - Class 3

Explore advanced techniques in Grasshopper for creating complex geometries, including grids, cells, and surface morphing. Hands-on exercises reinforce learning and practical application of concepts.

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

Fields Institute

Quotients of the Drury-Arveson Space and Their Classification in Terms of Complex Geometry

Explore quotients of Drury-Arveson space, their classification using complex geometry, and connections to hyperbolic metrics and holomorphic multipliers in this advanced mathematical lecture.

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

IMSA

Special Lecture Series on Numerical Geometry - Tristan Collins

Explore complete Calabi-Yau metrics on Fano manifolds with singular divisors, focusing on two-component cases and discussing potential generalizations to more complex scenarios.

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

IMSA

Canonical Metrics in Complex Geometry

Explore canonical metrics in complex geometry, focusing on pluriclosed and balanced metrics. Learn about new constructions of compact non-Kähler manifolds and their properties.

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

IMSA

Hyper-Kähler Manifolds - Part 1

Explore the foundations of hyper-Kähler manifolds, their connection to K3 surfaces, and key properties in this advanced mathematics lecture by renowned expert Claire Voisin.

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

IMSA

Quantum Representations and Bogomolov-Katzarkov Surfaces

Exploring quantum representations and their application to Bogomolov-Katzarkov surfaces, addressing the Shafarevich conjecture on holomorphic convexity in algebraic geometry.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

IMSA

Generalized Calabi-Yau Problem

Explore advanced concepts in generalized complex geometry, focusing on holomorphically trivial generalized canonical bundles, Calabi-Yau structures, and the current status of the Calabi-Yau problem.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

IMSA

Filtered Ends and Bochner Hartogs Dichotomy on Complete Kahler Manifolds

Explore filtered ends and Bochner Hartogs dichotomy on complete Kahler manifolds, examining relationships between generalized ends and first compactly supported cohomology.

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

ICTP Mathematics

Hyperkähler Manifolds: An Introduction - Part 4.1

Explore advanced concepts in complex geometry, focusing on Hyperkähler manifolds and their properties in this comprehensive mathematical lecture.

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

ICTP Mathematics

Hyperkähler Manifolds: An Introduction - Part 4.2

Explore advanced concepts of Hyperkähler manifolds with expert Elham IZADI, delving into complex geometric structures and their applications in mathematics and physics.

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

ICTP Mathematics

Hyperkähler Manifolds: An Introduction - Part 3.1

Explore advanced concepts in complex geometry, focusing on Hyperkähler manifolds and their properties in this in-depth mathematical lecture by Elham IZADI.

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

International Mathematical Union

Kähler Manifolds with Curvature Bounded Below

Explore Kähler manifolds with curvature bounded below, covering Yau's uniformization conjecture, compactification of manifolds, and Gromov-Hausdorff limits in this advanced mathematical survey.

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

International Mathematical Union

Xiaohua Zhu - Kähler-Ricci Flow on Fano Manifolds

Explore the Kähler-Ricci flow on Fano manifolds, delving into complex geometry and differential equations. Gain insights into this advanced mathematical topic through expert analysis and explanations.

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