Institute for Advanced Study Courses

Trust and Distrust in ML: Privacy, Verification and Robustness

Explore the critical aspects of machine learning trustworthiness with Shafi Goldwasser, examining privacy concerns, verification methods, and robustness challenges in this Emmy Noether Lecture.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

DAMAST - An Interactive Research Environment for Visualizing Multi-Religious Situations in the Islamicate World

Discover DAMAST, an interactive research environment visualizing multi-religious communities in the Islamicate world (600-1400 CE), featuring 8,300+ data points across 440+ locations with map, timeline, and filtering capabilities.

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

There Are Infinitely Many Elliptic Curves Over the Rationals of Rank 2

Explore the proof of infinitely many elliptic curves over the rationals with rank 2, using explicit models, 2-descent methods, and Tao-Ziegler theorem, with insights on rank stability.

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

Improved Fault-Tolerant Non-Clifford Gates - How to Multiply Quantumly

Explore fault-tolerant quantum computing with a focus on non-Clifford gates, examining new error-correcting code constructions that significantly reduce computational overhead, based on algebraic codes and expander graphs.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Language Generation in the Limit

Delve into the theoretical foundations of language generation with Jon Kleinberg, exploring adversarial models and contrasting generation with language identification in computational linguistics.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Mathematical Exploration and Discovery at Scale

Discover how AlphaEvolve uses AI to autonomously tackle mathematical problems across analysis, geometry, combinatorics, and number theory, revolutionizing discovery at unprecedented scale.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Improving Algorithmic Efficiency Using Cryptography

Discover how cryptographic primitives can accelerate computational algorithms beyond traditional methods, featuring trapdoor matrix distributions for faster matrix operations.

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

Disjoint Pairs in Set Systems and the Combinatorics of Low-Rank Matrices

Explore advanced combinatorial problems involving disjoint pairs in set systems and low-rank matrices, featuring solutions to longstanding questions by Daykin, Erdős, and others.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Rethinking Gravitational Instability as a Planet Formation Scenario

Explore how gravitational instability and dust dynamics work together to form planetary cores in young protostellar discs, challenging traditional planet formation theories.

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

Knot Types of Periodic Reeb Orbits and Their Role in 4-Dimensional Symplectic Topology

Explore knot types of periodic Reeb orbits in 4-dimensional symplectic topology and their constraints under dynamical convexity assumptions.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Slicing Spaces - From Contour Lines to Morse Theory: A Historical Perspective

Explore the historical development of Morse theory from 19th-century contour mapping to modern mathematical applications in this centennial tribute lecture.

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

Expressive Curves

Explore the concept of expressive curves in algebraic geometry, their criteria, constructions, and connections to plabic graphs, quivers, and links.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

On Triple Product L-Functions

Explore advanced techniques for proving analytic properties of triple product L-functions through generalized Poisson summation and the innovative fiber bundle method.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

The Hartle-Hawking Wavefunction and de Sitter Black Holes

Explore quantum aspects of black holes through the Hartle-Hawking wavefunction, examining Schwarzschild-de Sitter solutions and Euclidean Nariai geometry with new quantum corrections insights.

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

The Yes Boundaries Wavefunctions of the Universe and Late Time Cosmology

Explore advanced theoretical physics examining universe topology, timelike boundaries, and their role in holography and de Sitter cosmology through cutting-edge research.

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