Simons Institute Courses

Noise Stability - Beyond the Boolean Cube

Explore noise stability beyond the Boolean cube, analyzing stochastic processes and Brownian motion to derive new quantitative forms of Boolean analysis theorems.

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

Representation Theory in TCS and Extremal Combinatorics

Explore how Representation Theory extends Boolean function theory, leading to new insights in theoretical computer science and extremal combinatorics.

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

On Perfectly Friendly Bisections of Random Graphs

Explores vertex-isoperimetry expansion in random graphs, using boolean function tools to prove equipartition results with specific neighbor distribution properties across partitions.

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

Localization Schemes

Explore innovative localization schemes for analyzing Markov chain mixing times in continuous and discrete spaces, with applications to Ising models and Glauber dynamics.

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

Linearity Testing Over the Biased Cube

Explores linearity testing in p-biased settings, presenting a 4-query test with optimal soundness. Discusses structural results and direct product tests for functions correlated to linear functions under random restrictions.

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

PCPs and Global Hyper-contractivity - Lecture 2

Explore advanced concepts in PCPs and global hyper-contractivity with Dor Minzer, delving into complex mathematical theories and their applications in analysis and theoretical computer science.

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

PCPs and Global Hyper-contractivity - Lecture 1

Explore advanced concepts in theoretical computer science, focusing on Probabilistically Checkable Proofs and global hyper-contractivity with expert Dor Minzer.

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

Applications in Extremal Combinatorics - Lecture 1

Explore advanced concepts in extremal combinatorics, focusing on analytical techniques and their applications in theoretical computer science.

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

Hyper-contractivity in Analysis and Theoretical Computer Science - Introduction 3

Explore hyper-contractivity in analysis and theoretical computer science, examining its applications and implications for advanced mathematical concepts.

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

High-Dimensional Expanders - Lecture 2

Explore high-dimensional expanders with Irit Dinur, delving into advanced concepts and applications in analysis and theoretical computer science.

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

High-Dimensional Expanders - Lecture 1

Explore high-dimensional expanders with Irit Dinur, delving into advanced concepts in analysis and theoretical computer science.

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

High-Dimensional Expanders - Lecture 4

Explore advanced concepts in high-dimensional expanders, focusing on analysis techniques and applications in theoretical computer science.

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

High-Dimensional Expanders - Lecture 3

Explore advanced concepts in high-dimensional expanders, focusing on analysis techniques and applications in theoretical computer science.

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

Parallelism in Dynamic Graph Algorithms

Explore parallelism in dynamic data structures through batch algorithms and graph streaming, enabling efficient handling of concurrent updates and queries in graph algorithms.

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

Optimizing Dynamic-Graph Data Structures on Multicores with the Locality-First Strategy

Explore techniques for optimizing dynamic-graph data structures on multicores, focusing on locality-first strategies to enhance performance for large-scale problems in real-world applications.

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