Simons Foundation Courses

1/n - April 17, 2025

Dive into Nima Arkani Hamed's exploration of 1/n concepts in theoretical physics, examining fundamental principles and their implications for our understanding of the universe.

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

Non-Perturbative Aspects of Self-Dual Gauge Theory (April 17, 2025)

Explore non-perturbative aspects of self-dual gauge theory, including beta-function computations using Grothendieck-Riemann-Roch and holographic methods, with applications to QCD calculations without Feynman diagrams.

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

Celestial Holography and Self-Dual Einstein Gravity (April 17, 2025)

Delve into celestial holography and self-dual Einstein gravity through a variant model based on a CY 5-fold with K3 fibration over twistor space, exploring connections to four-dimensional gravitational theory.

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

Recent Advances in Stellarator Coil Optimization - March 21, 2025

Explore recent advances in stellarator coil optimization, including strain analysis, force calculations, and innovative methodologies using voxels, dipole arrays, and passive arrays.

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

Optimization and Engineering for EPOS - March 21, 2025

Dive into the optimization and engineering challenges of EPOS, a stellarator designed to trap electron-positron plasmas, exploring quasisymmetry, high-temperature superconducting coils, and integration with positron injection systems.

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

Turnstiles and Topological Index in Fusion Reactor Divertors

Explore the mathematical analysis of magnetic field topology in fusion reactors, focusing on turnstile mechanisms and their role in controlling plasma-wall interactions and optimizing divertor performance.

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

Full Flux Surface of Gyrokinetic Code, stella

Explore the full flux surface version of stella, a gyrokinetic code using pseudo-spectral methods to efficiently simulate plasma turbulence in complex magnetic geometries for fusion research, with enhanced computational efficiency.

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

Understanding Quasi-isodynamicity

Delve into the fundamentals of quasi-isodynamicity in magnetic field-plasma systems for fusion energy, exploring its characteristics, challenges, and practical applications in stellarator design through near-axis theory.

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

Recent Advances in Stellarator Coil Optimization - March 21, 2025

Explore recent advances in stellarator coil optimization, including strain analysis, force calculations, and innovative methodologies using voxels, dipole arrays, and passive arrays.

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

Design and Optimization of the Columbia Stellarator eXperiment

Explore the design and optimization of the Columbia Stellarator eXperiment (CSX), focusing on novel single-stage optimization techniques that simultaneously address plasma physics requirements and engineering constraints for fusion energy research.

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

The Non-Perturbative Adiabatic Invariant is All You Need

Discover a non-perturbative, data-driven averaging method for highly-oscillatory dynamical systems with marginal timescale separation, outperforming traditional asymptotic averaging in charged particle contexts.

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

Regularization and Convergence of the Near-Axis Expansion

Dive into the numerical analysis of the near-axis expansion for stellarator configurations, exploring regularization techniques that ensure convergence and examining the relationship between radius of convergence and axis-coil distance.

• YouTube
• 19 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