IAS | PCMI Park City Mathematics Institute Courses

Intersecting Families - Part 1

Discover the rich theory of intersecting families in combinatorics, exploring the Erdos-Ko-Rado theorem, Katona's t-intersecting theorem, and applications to Borsuk's conjecture.

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

Extremal Graph Theory - Part 1

Explore extremal graph theory fundamentals, focusing on H-free graphs and the maximum edge problem, with emphasis on challenging bipartite cases and recent mathematical breakthroughs.

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

Extremal Graph Theory - Part 2

Explore extremal graph theory focusing on bipartite graphs and the maximum edges in H-free graphs with n vertices, covering recent advances in this challenging area.

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

Intersecting Families - Part 1

Explore the rich theory of intersecting families in combinatorics, covering Erdős-Ko-Rado theorems, Katona's theorem, and applications to Borsuk's conjecture.

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

Intersecting Families - Part 2

Explore the rich theory of intersecting families in combinatorics, covering Erdős-Ko-Rado theorems, Katona's theorem, and applications to Borsuk's conjecture.

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

Asymptotic Enumeration via Graph Containers and Entropy - Part 1

Explore asymptotic enumeration techniques using graph containers and entropy methods for independent sets in expanders and hypergraphs.

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

Asymptotic Enumeration via Graph Containers and Entropy - Part 2

Explore advanced techniques combining graph containers and entropy methods for asymptotic enumeration problems in extremal and probabilistic combinatorics.

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

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