IAS | PCMI Park City Mathematics Institute Courses

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

Enumeration of Regular Graphs - Part 1

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

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

Arithmetic Ramsey Theory - Part 1

Explore arithmetic Ramsey theory fundamentals, covering van der Waerden's theorem and modern additive combinatorics tools to prove density and partition regularity of linear configurations.

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

Twisted Topological Tangles - The Knot Theory of Knitting

Explore the fascinating intersection of mathematics and ancient knitting technology, discovering how 1D yarn creates complex 2D materials through topological principles and slip knot structures.

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

Asymptotic Enumeration via Graph Containers and Entropy - Part 1

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

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

Asymptotic Enumeration via Graph Containers and Entropy - Part 5

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

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

Asymptotic Enumeration via Graph Containers and Entropy - Part 4

Explore advanced 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 3

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

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

From Sunflowers to Thresholds - Part 5

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

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