Simons Foundation Courses

Boundedness in General Type MMP

Explore boundedness properties in the Minimal Model Program for varieties of general type through advanced algebraic geometry techniques and recent developments.

• YouTube
• 56 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

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

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

Multiplicative Structure in Additive Problems

Explore Diophantine counting problems through circle method analysis, focusing on multiplicative statistics of polynomials and Perazzo cubic fourfolds with expert insights.

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

Distribution of Zeros, Eigenvalues and Eigenfunctions in Number Theory

Explore statistical laws governing zeta functions and automorphic forms, examining numerical observations and their impact on arithmetical invariants in number theory.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Universal Distributions of Groups and Algebraic Objects

Explore universal distributions of groups and algebraic structures in arithmetic statistics, from Cohen-Lenstra-Martinet heuristics to non-abelian groups and modules.

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

Joint Linnik Problems and Siegel Zeros

Explore advanced number theory through simultaneous equidistribution conjectures for torus embeddings in PGL_2 forms, connecting Siegel zeros to L-function bounds.

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

Extrema of the Characteristic Polynomial of CβE Matrices

Explore extrema of characteristic polynomials in CβE matrices and their logarithmically correlated fields, validating the Fyodorov–Hiary–Keating conjecture through rigorous mathematical analysis.

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