Complex Manifolds Courses and Certifications

Instituto de Matemática Pura e Aplicada

Special Holonomy and Geometric Structures on Complex Manifolds

Explore advanced geometric structures on complex manifolds, focusing on special holonomy and its connections to various mathematical fields and theoretical physics.

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

Instituto de Matemática Pura e Aplicada

Killing and Ricci-Hessian Equations in Pseudo-Kähler Geometry - Special Holonomy and Geometric Structures on Complex Manifolds

Explore Killing and Ricci-Hessian equations in (pseudo)Kähler geometry. Delve into special holonomy, complex manifolds, and their connections to various mathematical fields and theoretical physics.

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

Instituto de Matemática Pura e Aplicada

Special Holonomy and Geometric Structures on Complex Manifolds

Explore advanced topics in differential geometry, including special holonomy, complex manifolds, and their connections to various mathematical fields and theoretical physics.

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

Instituto de Matemática Pura e Aplicada

Special Holonomy and Geometric Structures on Complex Manifolds

Explore SU(2)-structure flows in complex manifolds, delving into special holonomy and geometric structures. Gain insights into differential geometry's connections with complex geometry, physics, and symplectic geometry.

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

IMSA

Hyperbolicity and Holomorphic Jet Differentials in Complex Manifolds

Delve into complex manifold hyperbolicity theory, exploring function theory, holomorphic jet differentials, and connections between geometric and number-theoretic approaches to rational points.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Fields Institute

Extension of 4-Dimensional Hamiltonian S1-Spaces Classification to Almost Complex Manifolds

Explore the classification of 4D Hamiltonian S1-spaces extended to almost complex manifolds, delving into advanced geometric concepts and their applications in mathematical physics.

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

ICTP Mathematics

Tautological Rings of Moduli Spaces of Curves - Lecture 3

Explore advanced concepts in algebraic geometry, focusing on tautological rings and their relation to moduli spaces of curves in this in-depth mathematical lecture.

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

IMSA

On Nilpotent Quotients of Quasi-Kähler Groups

Exploration of nilpotent quotients of quasi-Kähler groups, focusing on smooth complex quasi-projective manifolds and their quasi-Albanese maps, with implications for holomorphic convexity and special manifolds.

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

IMSA

Extensions in MHM and Hain's Biextension Line Bundle - Part 2

Explores biextension line bundles, their extensions, and algebraic structures. Presents a formula for Q-line bundles, building on Hain and Pearlstein's work on normal functions and complex manifolds.

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

IMSA

Extensions in MHM and Hain's Biextension Line Bundle - Part 1

Explore complex manifolds, biextension line bundles, and normal functions in algebraic geometry. Discover formulas for Q-line bundle extensions and their topological invariants.

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

International Centre for Theoretical Sciences

From Local to Global Holomorphic Peak Functions - Lecture 1

Explore holomorphic peak functions in complex analysis, from local to global perspectives. Gain insights into Cauchy-Riemann equations, L2-theory, and applications in higher-dimensional complex manifolds.

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

BIMSA

Recent Progress on Gamma Conjectures - ICBS 2024

Explore recent advancements in Gamma conjectures, including modifications to Gamma conjecture I and its application over Kähler moduli space.

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

BIMSA

Exotic Calabi-Yau Metric and Holomorphic Fibration

Explore complete Calabi-Yau metrics, from historical developments to recent constructions on C^3, with insights into collapsing metrics on Calabi-Yau 3-folds.

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

BIMSA

Ball Quotients and Algebraic Geometry - ICBS 2024

Explore ball quotients in algebraic geometry, focusing on moduli spaces, Kaehler metrics, and their connections to sporadic finite simple groups. Examine known examples and recent progress on the Allcock ball quotient.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Isolated and Parameterized Points on Algebraic Curves

Explore isolated and parameterized points on algebraic curves, examining their behavior in families and implications for elliptic curve arithmetic. Gain insights into curve geometry and its connection to arithmetic properties.

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