Simons Foundation Courses

Alfvénic Turbulence and Particle Acceleration

Explore the properties of Alfvénic turbulence in magnetized relativistic plasma, its role in particle acceleration, and its impact on astrophysical objects.

• YouTube
• 49 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

Neutron Stars: The Supranuclear Density Zombies of the Cosmos (March 26, 2025)

Explore how astrophysicists study neutron stars using various telescopes, from the International Space Station's X-ray telescope to large radio telescopes, revealing insights about these cosmic "zombies."

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

AI and AC: Learning Hardness in Mathematics and Artificial Intelligence

Explore the intersection of AI and mathematics as Sergei Gukov discusses "Learning Hardness," examining how solving difficult math problems drives both mathematical progress and AI advancement, with examples from knot theory and group theory.

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

Quiver-Like Varieties for the Geometric Categorification of Super-Algebras Gl(M|N) and the Associated Link Invariants - March 28, 2025

Explore string-theory inspired reinterpretations of Hamiltonian reduction in Nakajima quiver varieties and their connection to super-algebras gl(m|n) and link invariants.

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

From Link Homology to Topological Quantum Field Theories

Explore the connection between link homology and topological quantum field theories, examining how Khovanov's categorification of the Jones polynomial relates to higher-dimensional TQFTs.

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