Simons Foundation Courses

Sulfur Chemistry and Aerosol-Cloud Interactions Following SO2 Emissions from a Degassing Volcano

Explore sulfur chemistry and aerosol-cloud interactions in volcanic degassing, focusing on Taal volcano's SO2 emissions and their impact on cloud formation, radiation, and atmospheric processes.

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

Using Single Particle Measurements of Aerosols to Evaluate Candidate Materials for Solar Radiation Management

Explore how single-particle trapping and spectroscopy evaluate aerosol materials for solar radiation management, including sulfate, diamond, and metal-oxide particles under various conditions.

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

Modeling Atmospheric Turbulence and Its Impacts on Plume Dispersion for Stratospheric Aerosol Injection

Explore the modeling of atmospheric turbulence for stratospheric aerosol injection, examining how turbulence affects plume evolution and impacts climate cooling strategies and potential side effects.

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

Shock Formation and Maximal Hyperbolic Development in Multi-D Gas Dynamics

Explore the mathematical analysis of multi-dimensional compressible Euler equations, focusing on shock formation, maximal hyperbolic development, and the geometric framework for acoustic characteristic surfaces.

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

Formulation and Simulation of a Linear Dynamics Leading to a Loss of Regularity

Dive into the formulation of a linear model for fluid turbulence, exploring transport phenomena in Fourier space that generate irregular velocity fields from smooth ingredients through energy cascade across scales.

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

Propagation of Gaussianity and Application to the Incompressible Euler Dynamics

Delve into the propagation of Gaussianity in Hamiltonian equations, focusing on incompressible Euler dynamics and exploring how Gaussian initial data maintains Wick formula properties in large box regimes.

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

On the Wave Turbulence Theory of 2D Gravity Waves

Explore rigorous approaches to wave turbulence in water wave systems, focusing on quasilinear equations and new strategies combining deterministic energy estimates with dispersive propagation of randomness.

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

Odd Turbulence - December 5, 2025

Explore how turbulent cascades can be harnessed to generate patterns, with a focus on odd viscosity's role in creating tunable wavelength patterns in chiral fluids from bioactive to quantum systems.

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

Space-Time Dependence of Correlation Functions in Turbulence and Related Models - December 5, 2025

Explore the analytical approach to turbulence statistics using functional renormalization group, examining space-time correlation functions in Navier-Stokes equations and related simplified models like Kraichnan's model and stochastic Burgers equation.

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

The Evolution of Darwin's Finches (April 2, 2025)

Discover the dynamics of contemporary evolution through a 40-year study of Darwin's finches in the Galápagos, revealing how one species diversified into 18+ species over a million years.

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

The Hilbert Sixth Problem: Particles and Waves

Delve into the derivation of macroscopic equations from microscopic principles in Hilbert's sixth problem, examining both particle systems and wave turbulence through recent research on hard sphere models and nonlinear Schrödinger equations.

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

Machine-Precision Neural Networks for Multiscale Dynamics

Discover how multi-stage neural networks can achieve machine precision for scientific problems, overcoming traditional accuracy limitations and addressing spectral bias in multiscale dynamics and fluid dynamics.

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

From Quarks to Nuclei: Computing the Structure of Matter (April 23, 2025)

Explore how extreme-scale computation bridges particle physics to nuclear physics, including first-principles nuclear reaction calculations and new insights into proton pressure distribution.

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

Persistent Homology of Function Spaces and Geometric Metaphors in Biology

Explore persistent homology of function spaces, geometric metaphors in biology, and mathematical insights from biochemistry, including solutions to Gromov's problem and reflections on landscape and network concepts.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Complex Discrete Probability Models in Evolutionary Biology: Challenges and Opportunities

Explore complex discrete probability models in evolutionary biology, focusing on species phylogeny reconstruction from genomic data and the mathematical analysis of discordant gene histories.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video