Complex Analysis Courses and Certifications

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

Tom Rocks Maths

Helmholtz Principle and Vortex Motion

Explore Helmholtz' Principle and vortex motion in 2D potential flow. Learn about complex potentials, velocity fields, and the Method of Images to understand fluid dynamics and vortex trajectories.

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

Tom Rocks Maths

Building the Multiverse Library

Explore complex mathematics behind the Multiverse Library, focusing on branch cuts and multifunctions. Learn about holomorphic branches of complex logarithms and square root functions in this engaging mathematical journey.

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

Steve Brunton

Complex Analysis - Overview & Motivation, Complex Arithmetic, Euler's Formula & Polar Coordinates

Introduction to complex numbers, their arithmetic operations, Euler's formula, and polar coordinates. Covers solutions to differential equations and lays foundation for further complex analysis topics.

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

Hausdorff Center for Mathematics

Complex Monge-Ampère Operators and Functional Hermitian Intrinsic Volumes

Explore geometric construction of Monge-Ampère operators on finite convex functions, examining their properties and related valuations as functional versions of Hermitian intrinsic volumes.

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

Hausdorff Center for Mathematics

Numerical Approach to Polylogarithms on Higher-Genus Riemann Surfaces

Explore numerical evaluation of polylogarithms on genus-two Riemann surfaces using Schottky parametrization and averaging over genus-one differential forms, advancing particle physics research.

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

Insights into Mathematics

Bernhard Riemann and the Complex Sphere - Geometric Thinking in Mathematics

Explore Riemann's geometrical thinking on the complex sphere, from abstract discussions on mathematical space to practical applications in complex analysis and higher-dimensional geometry.

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

Institute for Pure & Applied Mathematics (IPAM)

Random Aggregation on the Complex Plane and the Hastings-Levitov Models

Explore random aggregation on complex planes through ALE models, including Hastings-Levitov models. Discover scaling limits, fluctuations, and connections to fundamental discrete models in statistical mechanics.

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

Fields Institute

Complex Rotation Numbers

Explore complex rotation numbers, their theory, dynamics, and applications in tame geometry and analysis. Delve into bubbles, self-similarity, and normalization concepts.

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

Fields Institute

Mini-course on Bergman Spaces - Part 1

Explore Bergman Spaces in mathematics, covering key concepts, theorems, and applications in analytic function theory. Gain insights from expert Stefan Richter.

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

Fields Institute

Hardy Spaces: Uniqueness and Harmonic Representation Theorems - Part 6

Explore uniqueness, harmonic representation, and representation theorems in Hardy spaces, advancing understanding of analytic function spaces and their applications.

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

Fields Institute

Mini-course on Hardy Spaces - Part 3

Explore Hardy spaces with a focus on rotation, generalization, and approximate identities. Delve into uniform boundedness, Poisson PR constructions, and harmonic functions.

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

Fields Institute

Mini-course on de Branges-Rovnyak Spaces - Part 1

Explore de Branges-Rovnyak spaces, covering history, multipliers, and types of spaces. Learn about Bronzerovnik and range spaces, general lemmas, and boundary behavior.

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

Fields Institute

Carathéodory Balls and Proper Holomorphic Maps on Multiply-Connected Planar Domains

Explore Carathéodory balls and proper holomorphic maps on multiply-connected planar domains, focusing on circular domains, proper maps, and related mathematical concepts.

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

Fields Institute

Mini-course on Blaschke Products and Inner Functions - Part 1

Explore Blaschke products and inner functions in complex analysis, covering definitions, singular inner functions, and dynamical properties in this advanced mathematics lecture.

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