Asymptotic Analysis Courses and Certifications

International Centre for Theoretical Sciences

Gamma Convergence - Lecture 2

Explore gamma convergence, minimization problems, and homogenization in this advanced mathematics lecture. Learn about coercivity, lower semicontinuity, and integral functions in the context of multi-scale analysis.

• YouTube
• 1 hour 30 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Random Matrix Theory and Its Applications - Lecture 5

Explore advanced random matrix theory concepts, including Gaussian ensembles, coarse-graining techniques, and the Wigner semi-circular law in this comprehensive lecture.

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

International Mathematical Union

Sylvie Méléard- Multiscale Eco-Evolutionary Models- From Individuals to Populations

Exploring eco-evolutionary models from individual to population scales, focusing on small population effects, mutation dynamics, and long-term behaviors using stochastic processes and mathematical approximations.

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

Hausdorff Center for Mathematics

Helmut Abels - Diffuse and Sharp Interface Models for Two Phase Flows

Overview of analytic results for diffuse and sharp interface models in two-phase flow, discussing asymptotic limits as interfacial thickness approaches zero and exploring rigorous analytic results for sharp interface limits.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Asymptotics for the Lower Tail of the KPZ Equation

Exploration of asymptotic behavior in the KPZ equation's lower tail, covering motivation, proofs, and generalizations for advanced mathematics researchers.

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

ICTP Mathematics

Random Matrices and the Uses of Dyson-Schwinger Equations - III

Explore advanced topics in random matrix theory, including Dyson-Schwinger equations, operator algebra, and central limit theorems, with applications in mathematical physics.

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

ICTP Mathematics

Asymptotics of Orthogonal Polynomial Ensembles via Integrable Methods

Explore statistical properties of random matrices and point processes, focusing on asymptotics of orthogonal polynomial ensembles and their applications in various fields of mathematics and physics.

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

International Mathematical Union

Hydrodynamic Stability at High Reynolds Number and Transition Threshold Problem

Explores hydrodynamic stability theory, focusing on laminar flow instability and turbulence transition at high Reynolds numbers. Discusses key physical effects and recent progress in linear inviscid damping and enhanced dissipation for shear flows.

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

Society for Industrial and Applied Mathematics

From Newton to Boltzmann - Fluctuations and Large Deviations in Hard Sphere Gas Dynamics

Explore macroscopic fluctuations in hard sphere gases, including deviations from the Boltzmann equation, central limit theorem, and large deviation bounds in the Boltzmann-Grad limit.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Society for Industrial and Applied Mathematics

Normalization Effects on Neural Networks: Generalization and High-Dimensional Applications - SIAM FME Talk

Exploring neural network performance, normalization effects, and high-dimensional PDE solving using deep learning. Insights on generalization properties and applications in mathematical finance.

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

Fields Institute

Transseries, Model Theory, and Hardy Fields - Lecture 14

Explore advanced mathematical concepts in transseries, model theory, and Hardy fields with expert Lou van den Dries in this graduate-level lecture from the Fields Institute.

• YouTube
• 1 hour 37 minutes
• Self-Paced
• Free Video

Fields Institute

Transseries, Model Theory, and Hardy Fields - Lecture 9

Explore advanced mathematical concepts in transseries, model theory, and Hardy fields with Professor Lou van den Dries in this graduate-level lecture from the Fields Institute.

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

Fields Institute

Surreal Numbers and Transseries - Lecture 3

Explore advanced mathematical concepts of surreal numbers and transseries, delving into their properties, applications, and connections to asymptotic analysis.

• YouTube
• 1 hour 44 minutes
• Self-Paced
• Free Video

Fields Institute

Surreal Numbers and Transseries - Lecture 2

Explore advanced mathematical concepts of surreal numbers and transseries, delving into their properties and applications in asymptotic analysis.

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

Fields Institute

Transseries, Model Theory, and Hardy Fields - Lecture 1

Explore advanced mathematical concepts in transseries, model theory, and Hardy fields with Professor Lou van den Dries in this graduate-level lecture series.

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