IAS | PCMI Park City Mathematics Institute Courses

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

Mathematics and Physics in Creative Crafts - From Curvature to Knot Theory

Explore the fascinating intersection of mathematics and crafting, discovering how physics, geometry, and knot theory connect with crochet, quilting, and textile manufacturing patterns.

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

Mathematical Maturity - Story vs Craft - Why I Like to Lecture

Explore the philosophical debate between storytelling and craftsmanship in mathematics education through an engaging lecture that challenges traditional teaching perspectives.

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

Arithmetic Properties of Local Systems in Motivic Homotopy Theory

Delve into fundamental group theory and local systems in arithmetic geometry, exploring classical conjectures and recent developments in motivic representations and their arithmetic properties.

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

Motivic Explorations in Enumerative Geometry - Part 4

Delve into advanced enumerative geometry concepts, exploring Bézout's theorem, tropical geometry, and motivic homotopy theory applications for solving geometric problems over arbitrary fields.

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