IAS | PCMI Park City Mathematics Institute Courses

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

Graph-Codes - Problems, Results and Methods

Explore how binary vectors as graph edge-sets transform coding theory into extremal graph problems, combining combinatorial, probabilistic, and information theory methods.

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

Sublinear Expander Graphs - Part 2

Explore sublinear expansion theory and its applications in graph theory, building on Komlós-Szemerédi's foundational work from the 90s.

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

Sublinear Expander Graphs - Part 1

Explore sublinear expander graphs, a weaker notion of expansion with remarkable applications in recent combinatorics research and their connections to probability theory.

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

Statistical Physics Approach to Asymptotic Enumeration and Large Deviations in Random Graphs - Part 2

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

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

Ramsey Theory on Graphs - Part 1

Explore fundamental methods in modern combinatorics through Ramsey theory on graphs, covering key techniques used throughout combinatorics and beyond.

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

Statistical Physics Approach to Asymptotic Enumeration and Large Deviations in Random Graphs - Part 1

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

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

Statistical Physics Approach to Asymptotic Enumeration and Large Deviations in Random Graphs - Part 3

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

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

Ramsey Theory on Graphs - Part 2

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

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