Mathematical Physics Courses and Certifications

International Centre for Theoretical Sciences

Is the Universe Geometric or Algebraic? by Minhyong Kim

Explore the interplay between geometry and algebra in understanding the universe, from ancient concepts to modern physics, with insights on perception, reality, and mathematical foundations.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Computational Theory of Riemann-Hilbert Problems - Lecture 1

Explore computational approaches to Riemann-Hilbert problems, covering key concepts like Cauchy integrals and analytic functions. Gain insights into this fundamental topic in mathematical physics.

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

Institute for Advanced Study

Inverse Problems for Quantum Graphs - Pavel Kurasov

Explore inverse problems for quantum graphs, covering Ambartsumian-type results, trace formulas, and implications for various graph structures. Gain insights into local inverse problems and explicit formulas.

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

Institute for Advanced Study

The Nonlinear Stability of the Schwarzschild Metric Without Symmetry - Mihalis Dafermos

Explore the nonlinear stability of the Schwarzschild metric in general relativity, covering key concepts, theorems, and challenges in mathematical physics and black hole dynamics.

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

Institute for Advanced Study

Extreme Eigenvalue Distributions of Sparse Random Graphs - Jiaoyang Huang

Explore extreme eigenvalue distributions in sparse random graphs, covering empirical distributions, edge expansion, routing graphs, and universal properties. Gain insights into mathematical physics and graph theory.

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

Institut des Hautes Etudes Scientifiques (IHES)

Singular Stochastic PDE: More Geometry and Less Combinatorics

Explore singular stochastic PDEs through a geometric approach, focusing on renormalization, symmetry preservation, and Malliavin derivatives for characterizing expansions without divergent terms.

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

NPTEL-NOC IITM

Introduction to Green's Function: Motivations for Green's Functions

Explore Green's functions and their motivations in mathematical physics, gaining insights into solving differential equations and boundary value problems.

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

NPTEL-NOC IITM

Introduction to Green's Function: 2-D Example - Evaluating Constants - Part 2

Explore advanced concepts in Green's Function for 2D problems, focusing on evaluating constants in the second part of this mathematical analysis.

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

NPTEL-NOC IITM

Introduction to Green's Function: 1-D Example - Alternate Representation

Explore alternate representations of Green's Function in 1-D, focusing on practical applications and problem-solving techniques in mathematical physics.

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

NPTEL-NOC IITM

Legendre Polynomials: Rodrigues Formula, Orthogonality, and Normalization Integral - Lecture 48

Explore Legendre polynomials, including Rodrigues formula, orthogonality, and normalization integral, to enhance your mathematical understanding.

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

Mathemaniac

Different Forces, Same Elliptical Orbits - Coincidence? - Hidden Gems #2

Explore the surprising mathematical connection between Newtonian gravity and Hooke's law through their shared elliptical orbits, uncovering Newton's geometric insights.

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

NPTEL-NOC IITM

Introduction to Green's Function - A One-Dimensional Example

Explore Green's Function through a one-dimensional example, gaining insights into this mathematical concept and its applications in physics and engineering.

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

Michael Penn

The Quantum Integral

Explore the fascinating concept of quantum integrals, delving into their mathematical properties and applications in advanced physics and quantum mechanics.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Nonlinear Waves and Relativity

Explore advanced mathematical physics through dispersive PDEs and general relativity, covering scattering theory, wave equations, and spacetime dynamics in this comprehensive program.

• YouTube
• 22 hours 20 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Riemann-Hilbert Problems - Theory and Applications

Dive into Riemann-Hilbert problems theory, inverse scattering, nonlinear steepest-descent methods for integrable systems, random matrices, and orthogonal polynomials applications.

• YouTube
• 4 hours 14 minutes
• On-Demand
• Free Video