Max Planck Science Courses

Global Guarantees for Policy Gradient Methods

Explore global guarantees for policy gradient methods in reinforcement learning, examining theoretical foundations and practical implications.

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

Shuffling-based Stochastic Optimization Methods: Bridging the Theory-practice Gap

Explore shuffling-based stochastic optimization methods and their practical applications in bridging theoretical concepts with real-world implementation.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Generic Alignment Conjecture and the Problem of Emergence of Collective Behavior

Explore compressible and incompressible flows, focusing on collision avoidance, velocity matching, and flock centering in collective behavior emergence.

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

Anomalous Dissipation and the Strong Onsager Conjecture - Part 3: From Fourier Series to Wavelet Series

Explore advanced concepts in turbulent flows, focusing on anomalous dissipation and the Strong Onsager Conjecture. Delve into mathematical techniques transitioning from Fourier to wavelet series analysis.

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

Anomalous Dissipation and the Strong Onsager Conjecture - Part 2: L^3 Convex Integration

Explore anomalous dissipation and the Strong Onsager Conjecture in turbulent flows, focusing on L^3 convex integration techniques for mathematical analysis of energy transfer.

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

Anomalous Dissipation and the Strong Onsager Conjecture - Part 1: The Local Energy Inequality

Explore anomalous dissipation and the Strong Onsager Conjecture, focusing on local energy inequality in turbulent flows and energy transfer between scales.

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

Anomalous Dissipation and the Strong Onsager Conjecture - Part 4: Error Estimates

Explore error estimates in anomalous dissipation and the Strong Onsager Conjecture, delving into mathematical descriptions of turbulent flows and energy transfer between scales.

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

Anomalous Dissipation and the Strong Onsager Conjecture - Part 5: Intermittent Pressure

Explore anomalous dissipation and the Strong Onsager Conjecture, focusing on intermittent pressure in turbulent flows. Delve into energy transfer mechanisms and mathematical descriptions of turbulence.

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

Mathematical General Relativity to Quantum Field and Information Theory - Research Overview

Explore core research in Mathematical General Relativity, Quantum Field Theory, and Information Theory, with connections to various mathematical areas.

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

Fluid Equations: From Leray to Ladyzhenskaya and Beyond

Explore incompressible fluid theory, from Leray's weak solutions to Ladyzhenskaya's contributions, and recent findings on Navier-Stokes equations and turbulence.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Statistical Manifolds and F-Manifold Structure in Exponential Families

Explore statistical manifolds' F-manifold structure, connecting information geometry to Frobenius manifolds and revealing rich algebraic and geometrical properties.

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

Riemann's Theta Function: From Algebraic Geometry to Water Wave Physics

Explore Riemann's theta function's role in mathematics, from geometry to cryptography, and its connection to water wave physics through the KP equation.

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