Simons Foundation Courses

Evolving Perspectives on Autism

2 ratings

Explore the changing scientific understanding of autism spectrum disorders, their diagnosis, and treatment approaches through historical and contemporary research perspectives.

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

Evolution of the Cerebral Cortex: From New Types of Neurons to New Cognitive Functions (March 19, 2025)

Explore the evolution of neuron types in the cerebral cortex, examining how developmental processes and gene expression variations led to diverse cortical architectures and functions.

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

Verified Collaboration: How the Lean Project is Transforming Mathematics, Programming, and AI

Explore how the Lean project revolutionizes mathematics, programming, and AI through verified collaboration, enabling rigorous proof verification and creating foundations for more reliable scientific AI systems.

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

P-Adic Cohomologies Using Homotopy Theory (March 13, 2025)

Delve into how non-Archimedean motivic homotopy theory can define rational p-adic cohomology theories, exploring relative rigid cohomology, Hyodo-Kato cohomology, and motivic nearby cycles with Alberto Vezzani.

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

Perfectoid Pure Singularities (March 13, 2025)

Explore the concept of perfectoid pure singularities, their relationship to F-pure rings, and connections to log canonical singularities through examples and theoretical properties.

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

Intersection Cohomology of Shimura Varieties (March 13, 2025)

Explore the intersection cohomology of Shimura varieties and its relation to automorphic forms through L2 cohomology, with insights from the Fargues-Scholze local Langlands correspondence.

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

On Hopkins' Picard Group - March 13, 2025

Delve into the study of Picard groups in K(n)-local spectra and chromatic homotopy theory, exploring recent computational advances using p-adic geometry and Drinfeld's symmetric space.

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

Applications of F-gauges - March 13, 2025

Explore Bhatt–Lurie and Drinfeld's theory of F-gauges and their diverse applications in algebra, geometry, and topology with Toby Gee.

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

Prismatic Stable Homotopy Theory (March 14, 2025)

Explore trace methods in algebraic K-theory and their potential extension to other cohomological invariants in algebraic geometry with Jacob Lurie's analysis of prismatic stable homotopy theory.

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

On the Bloch–Kato Conjecture for Some Four-Dimensional Symplectic Galois Representations - March 14, 2025

Delve into Naomi Sweeting's exploration of the Bloch-Kato Conjecture for four-dimensional symplectic Galois representations, examining the relationship between Selmer ranks and L-function vanishing orders through ramified Galois cohomology classes.

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

Harish-Chandra Characters and the Langlands Conjectures (March 13, 2025)

Delve into Harish-Chandra's character theory for reductive groups, exploring recent formulas for p-adic groups, parallels with real cases, and implications for the refined local Langlands correspondence.

• YouTube
• 54 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
• 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