Kähler Geometry Courses and Certifications

Centre International de Rencontres Mathématiques

Analytic Delta Invariant and Weighted Kähler Geometry - Lecture 2

Delve into the analytic delta invariant and weighted Kähler geometry with Thibaut Delcroix as he extends his framework to handle Kähler-Ricci solitons, building on his previous lecture about K-stability of Fano varieties.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Analytic Delta Invariant and Weighted Kähler Geometry - Lecture 1

Delve into the analytic viewpoint on the delta invariant in Fano varieties and explore the variational approach to canonical Kähler metrics with Thibaut Delcroix's mathematical lecture on K-stability.

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

Institut des Hautes Etudes Scientifiques (IHES)

The Einstein Equation in Kähler Geometry

Explore how the Einstein equation simplifies in Kähler geometry and discover recent advances beyond Yau's theorem, including diameter estimates and convergence theorems.

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

Centre International de Rencontres Mathématiques

Kähler Families of Green's Functions

Explore uniform estimates for Green's functions in Kähler forms, extending works by Guo, Phong, Song, and Sturm, with applications to diameter bounds and non-collapsing estimates for canonical Kähler metrics.

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

BIMSA

Convexity of the Mabuchi K-Energy and Uniqueness of Extremal Metrics

Explore the mathematical relationship between Mabuchi K-energy convexity and the uniqueness properties of extremal metrics in complex geometry.

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

BIMSA

Complex Brunn-Minkowski Theory and Uniqueness Theorems in Kähler Geometry

Explore complex Brunn-Minkowski theory and its applications in Kähler geometry, focusing on uniqueness theorems and generalizations of Bando-Mabuchi's work on Kähler-Einstein metrics.

• YouTube
• 46 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

Institute for Advanced Study

From the Universality to the Kähler Geometry of Random Curves

Explore the connection between random curve universality and Kähler geometry through SLE theory, Loewner energy, and applications to quantum gravity and holographic principles.

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

Institut des Hautes Etudes Scientifiques (IHES)

Geometry in Non-Positive Curvature and Kähler Groups

Explore advanced geometric group theory through expert lectures on hyperbolic geometry, Kähler groups, and their interactions in this specialized mathematical conference.

• YouTube
• 10 hours 11 minutes
• On-Demand
• Free Video

Harvard CMSA

Special Kähler Geometry and Collapsing

Explore special Kähler geometry's role in supersymmetric gauge theories and mirror symmetry, focusing on hyperkähler manifolds with algebraic integrable systems and metric collapse.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

IMSA

Extending Hodge Polynomials to Non-Kähler Geometry

Delve into advanced mathematical concepts exploring Hodge polynomials beyond Kähler geometry, examining LVMB manifolds and motivic properties through pluri-logarithmic transforms.

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

BIMSA

Canonical Kähler Metrics and Infinite-Dimensional Geometry

Explore canonical Kähler metrics through infinite-dimensional geometry perspectives in this advanced mathematical lecture by Tamas Darvas.

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

Fields Institute

Symplectic Geometry

Master symplectic manifolds, Darboux theorem, Hamiltonian mechanics, moment maps, and advanced topics like toric varieties, quantization, and mirror symmetry in this comprehensive mathematical framework.

• YouTube
• 1 day 11 hours 57 minutes
• On-Demand
• Free Video

ICTP Mathematics

Hyperkähler Manifolds: An Introduction - Part 1

Explore the intricacies of hyperkähler manifolds in this advanced algebraic geometry lecture, delving into classical concepts and recent developments in the field.

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

ICTP Mathematics

Hyperkähler Manifolds: An Introduction - Part 5

Explore advanced concepts in algebraic geometry, focusing on hyperkähler manifolds and their properties in this in-depth lecture by Elham Izadi.

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