IAS | PCMI Park City Mathematics Institute Courses

Ramsey Theory on Graphs - Part 5

Explore fundamental methods in modern combinatorics through Ramsey theory on graphs, covering techniques that have influenced combinatorics and beyond.

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

Statistical Physics Approach to Asymptotic Enumeration and Large Deviations in Random Graphs - Part 5

Explore statistical physics tools like Gibbs measures and partition functions to solve asymptotic enumeration problems and analyze large deviations in random graphs.

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

Sublinear Expander Graphs - Part 5

Explore sublinear expander graphs and their remarkable applications in combinatorics, building from basic expansion theory to advanced decomposition techniques.

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

Sublinear Expander Graphs - Part 3

Explore sublinear expander graphs, their properties, and applications in combinatorics through advanced graph theory concepts and probabilistic methods.

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

A World from a Sheet of Paper - Exploring Phenomena Through Folding, Stacking, and Origami

Discover the fascinating world of paper folding, exploring magic tricks, geometry, elasticity, and origami through hands-on demonstrations you can recreate at home.

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

Statistical Physics Approach to Asymptotic Enumeration and Large Deviations in Random Graphs - Part 4

Explore statistical physics tools like Gibbs measures and partition functions to solve asymptotic enumeration problems and analyze large deviations in random graphs.

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

Ramsey Theory on Graphs - Part 3

Explore fundamental methods in modern combinatorics through Ramsey theory on graphs, covering techniques that have influenced combinatorics and beyond.

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

Sublinear Expander Graphs - Part 4

Explore sublinear expander graphs and their remarkable applications in combinatorics through advanced graph theory, probability, and linear algebra techniques.

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

Enumeration of Regular Graphs - Part 3

Explore asymptotic enumeration techniques for regular graphs using configuration models, generating functions, and Stein's method with applications to network design and modeling.

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

From Sunflowers to Thresholds - Part 3

Explore the sunflower conjecture and its surprising connections to computational complexity and threshold phenomena in this advanced combinatorics lecture.

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

Machine Learning and Pure Math - Especially Extremal Combinatorics

Explore how machine learning techniques can solve complex problems in extremal combinatorics, from constructing large capsets to finding graphs with specific properties.

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

Arithmetic Ramsey Theory - Part 2

Explore advanced Ramsey-theoretic questions in abelian groups, covering van der Waerden's theorem and modern additive combinatorics tools for density and partition regularity.

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

Enumeration of Regular Graphs - Part 2

Explore advanced asymptotic enumeration techniques for regular graphs, focusing on Stein's method and degree switchings with applications to network design and modeling.

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

From Sunflowers to Thresholds - Part 2

Explore major breakthroughs in the sunflower conjecture and its surprising connections to computational complexity and threshold phenomena, leading to the Kahn-Kalai conjecture resolution.

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

From Sunflowers to Thresholds - Part 1

Explore the sunflower conjecture and its surprising connections to computational complexity and threshold phenomena in this mathematical lecture.

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