Simons Foundation Courses

Blueprints and Prime Number Theorem

Discover blueprint technology and Prime Number Theorem formalization techniques in Lean, focusing on collaborative mathematical proof development and advanced metaprogramming methods.

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

Metaprogramming in Lean - Talk 1

Discover metaprogramming fundamentals in Lean through expert guidance from Heather Macbeth at this advanced mathematical formalization workshop.

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

Doing Elementary Number Theory in Lean - Talk 2

Explore elementary number theory formalization in Lean through practical exercises covering rings, unique factorization domains, congruence, finite fields, and quadratic reciprocity.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Prime Number Theorem - June 23, 2025

Explore advanced formalization techniques in Lean through the Prime Number Theorem project with expert guidance from Alex Kontorovich at this specialized workshop session.

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

Doing Elementary Number Theory in Lean - Talk 1

Discover how to formalize elementary number theory concepts in Lean, covering rings, unique factorization domains, congruence, finite fields, and quadratic reciprocity through hands-on exercises.

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

Structures

Explore mathematical structures through Lean formalization, focusing on algebra and number theory concepts including rings, unique factorization domains, and quadratic reciprocity.

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

First Geometry Lecture - Group Actions on Affine Space and Euclidean Space

Explore group actions on affine and Euclidean spaces through formalization in Lean, building undergraduate-level geometry skills with mathematical proof verification.

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

First Analysis Lecture - Sequences, Series, Limits, and Continuity

Master mathematical analysis concepts including sequences, series, limits, and continuity while learning to formalize proofs in Lean programming language for rigorous mathematical reasoning.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Robin Green Functions and the Shape of Lungs

Explore how mathematical diffusions with Robin boundary conditions reveal the fractal geometry and oxygen absorption properties of mammalian lung structures.

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