Monge-Ampère Equation Courses and Certifications

Banach Center

Monge-Ampère's Equation in Hypercomplex Geometry

Explore Monge-Ampère's equation in hypercomplex geometry, delving into advanced mathematical concepts and their applications.

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

BIMSA

Second Order Interior Estimates of Monge-Ampere Type Equations

Explore interior second order derivative estimates for Monge-Ampere type equations, focusing on partial structure cases using Pogorelov estimates and Legendre transforms.

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

BIMSA

A Survey on Generalized Monge-Ampère Equations and Subvarieties

Explore advanced mathematical concepts in generalized Monge-Ampère equations and their connections to algebraic geometry through subvarieties analysis.

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

Stony Brook Mathematics

Monge-Ampere Equations: Beyond the Classical Cases

Delve into advanced mathematical theory exploring octonionic Monge-Ampère equations, their applications in geometry, and groundbreaking developments in 16-manifolds and Calabi-Yau theorem extensions.

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

Hausdorff Center for Mathematics

Convergent Semi-Lagrangian Methods for the Monge-Ampère Equation on Unstructured Grids

Explores semi-Lagrangian discretisation of Monge-Ampère operator on P1 finite element spaces, discussing challenges and solutions for numerical methods in solving Monge-Ampère equations, with applications in inverse reflector problems.

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

Fields Institute

The Universal Beltrami Equation and Its Interaction with the Monge-Ampère Equation and the Scaling Limits of Random Structures

Explore the universal Beltrami equation's connections to Monge-Ampère equations and random structure scaling limits in this advanced mathematical analysis.

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

几何中的一类非线性四阶PDE

本课程以几何为出发点来介绍一类线性化的 Monge-Ampere 方程，即仿射几何中的极大曲面方程和环簇几何中的数量曲率方程。通过课程，希望研究生能快速进入几何的相关问题研究。

• XuetangX
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

Multiscale Problems - Algorithms, Numerical Analysis and Computation

Explore advanced mathematical techniques for solving complex multiscale problems through expert lectures on numerical analysis, finite element methods, and computational algorithms.

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

ICTP Mathematics

Geometric Measure Theory and Optimal Transport

Explore advanced mathematical concepts connecting geometric measure theory with optimal transport through expert lectures on regularity theory, Monge-Ampère equations, and stability results.

• YouTube
• 1 day 7 hours 45 minutes
• On-Demand
• Free Video

ICTP Mathematics

Optimal Transportation, Monge-Ampère Equations and Riemannian Ricci Bounds - Lecture 1

Explore optimal transportation, Monge-Ampère equations, and Riemannian Ricci bounds in this advanced mathematics lecture by L. Ambrosio from Scuola Normale Superiore di Pisa.

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

ICTP Mathematics

Introduction to Optimal Transportation and Monge Ampère Type Equations - Lecture 2

Explore optimal transportation and Monge Ampère equations, covering key concepts like super differentials, isoperimetric problems, and probability measures in this advanced mathematics lecture.

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

Hausdorff Center for Mathematics

Two-Scale FEMs for Non-Variational Elliptic PDEs

Explore advanced finite element methods for non-variational elliptic PDEs, focusing on two-scale approaches, monotonicity enforcement, and novel error estimation techniques for complex mathematical problems.

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

International Centre for Theoretical Sciences

The Monge-Ampère Equations and the Bergman Kernel - Lecture 1

Explore complex analysis in higher dimensions, focusing on Cauchy-Riemann equations, L2 theory, and applications to geometry. Learn about Bergman kernels and extension theorems in this advanced mathematics lecture.

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

BIMSA

A Nonlinear Least-squares Finite Element Method for the Monge-Ampere Equation

Explore a nonlinear least-squares finite element method for solving the Monge-Ampere equation, focusing on smooth convex solutions and innovative degrees of freedom.

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

IMSA

SYZ for Hypersurfaces of Toric Fano Manifolds and Optimal Transport - Part 1

Delve into the relationship between SYZ-conjecture, Calabi-Yau hypersurfaces, and optimal transport theory through advanced mathematical analysis of Monge-Ampère equations and toric geometry.

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