Simons Foundation Courses

Evolving Perspectives on Autism

1 rating

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

Databases and Discovery in Arithmetic

Explore how mathematical datasets are created, maintained, and their potential for breakthroughs in arithmetic research with Brendan Hassett's Presidential Lecture.

• YouTube
• 53 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

ASD Connections and Cosmetic Surgery - March 28, 2025

Delve into the cosmetic surgery conjecture in 3-manifolds, exploring how instanton homology rules out certain surgery cases, leaving only the possibility of 2-surgery, with discussion of limitations and future developments.

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

Exotic Phenomena in Dimension 4 - March 27, 2025

Explore the mysterious world of exotic smooth 4-manifolds with Lisa Piccirillo, examining methods to identify distinct smooth structures with identical topological types.

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

SO(3) Versus SU(3) in the Instanton Homology for Webs and Foams - March 27, 2025

Explore the relationship between SO(3) and SU(3) gauge theories in instanton homology for webs and foams, examining how replacing SO(3) with SU(3) affects structure and results.

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

Real Heegaard Floer Homology - March 27, 2025

Delve into the construction of real Heegaard Floer homology for 3-manifolds with involution, exploring its topological invariance, connections to Miyazawa's work, and applications to exotic RP^2-knots.

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

Smooth Structures on Closed Four-Manifolds with Non-Trivial Fundamental Group - March 27, 2025

Explore key constructions for producing 'exotic' smooth structures on closed four-manifolds with non-trivial fundamental groups, examining sources of exoticness through the genus function on second homology groups.

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

Lifting Swing Surfaces to AdS

Delve into the holographic duality between BMS field theory entanglement entropy and swing surfaces, as Sabrina Pasterski lifts this construction to AdS/CFT.

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

A Background Independent Algebra in Quantum Gravity (April 18, 2025)

Explore the algebra of observables along an observer's worldline as a background independent algebra in quantum gravity with Edward Witten.

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

Classical Gravitational Wave Tails from Soft Theorem (April 18, 2025)

Explore how classical soft graviton theorem determines gravitational wave patterns from colliding objects in space, including power law fall-off and logarithmic corrections, with potential applications.

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

The TsT/TTbar Correspondence: A Top-Down Approach of Non-AdS Holography

Explore the TsT/TTbar correspondence as a non-AdS holography model derived from string theory, examining its spectrum, black holes, symmetries, and correlation functions in relation to TTbar-deformed CFT.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Holograms in Asymptotically Flat Space (April 17, 2025)

Explore generalized entanglement wedges in asymptotically flat spacetimes, examining their boundaries and complementarity with Raphael Bousso's insights from joint research works.

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