Institute for Pure & Applied Mathematics (IPAM) Courses

Dimer Models and Random Tilings - Part 2

Explore dimer models, perfect matchings, and tilings with advanced mathematical tools. Delve into Kasteleyn's theory, combinatorial correspondences, and asymptotic methods for large-scale limits.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Symmetric Functions: Formulas, Combinatorial Models, and Applications - Part 2

Explore advanced concepts in symmetric functions, their applications in combinatorics and representation theory, and their role in statistical mechanics as partition functions.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Local Weak Convergence for Random Constraint Satisfaction Problems

Explore local weak convergence in random constraint satisfaction problems with Princeton's Allan Sly, delving into advanced statistical mechanics concepts beyond two dimensions.

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

Random Aggregation on the Complex Plane and the Hastings-Levitov Models

Explore random aggregation on complex planes through ALE models, including Hastings-Levitov models. Discover scaling limits, fluctuations, and connections to fundamental discrete models in statistical mechanics.

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

Epidemics on Large Networks - Phase Transitions and Survival Time

Explore epidemic models on large networks, focusing on phase transitions in survival time for deterministic and random graphs. Recent progress and open questions discussed.

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

Homological Percolation in a Torus

Explore homological percolation on tori, examining phase transitions in higher dimensions using algebraic topology. Discover new perspectives on percolation beyond traditional giant components.

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

The Arboreal Gas - Percolative Properties of Random Forests

Explore the percolative properties of random forests in the arboreal gas model, examining the formation of giant trees and its applications to branched polymer gelation.

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

The Plaquette Random Cluster Model and Potts Lattice Gauge Theory

Explore phase transitions in Potts lattice gauge theory, focusing on Wilson loop expectations and their transition from area to perimeter law, using a generalized random cluster model approach.

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

Poisson-Dirichlet Distribution for the Interchange Process in Five Dimensions

Explores the emergence of macroscopic cycles in the interchange process on high-dimensional tori, proving convergence to Poisson-Dirichlet distribution for cycle lengths in dimensions 4 and above.

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

Scaling Exponents in Stationary Random Graphs

Explore scaling exponents in stationary random graphs, examining relationships between fractal dimension, walk dimension, resistance, spectral dimension, and extremal growth in statistical physics.

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

Spectral Gap Estimates for the Random Field Ising Model - Lecture

Spectral gap estimates for random field Ising model: convergence rates, Glauber dynamics, Griffiths phase. Combines stochastic localization and percolation-theoretic coarse-graining techniques.

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

Dimers in 3D - Large Deviations Principle and Statistical Mechanics

Explore 3D dimer tilings and their large deviations principle, comparing with 2D results and examining unique challenges in higher dimensions through simulations and mathematical insights.

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

Distances in Hierarchical Percolation

Explore hierarchical percolation's behavior across dimensions, examining chemical, extremal, and pivotal distances in high and upper-critical dimensions through renormalization group analysis.

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

Minimal Surfaces in Random Environment

Explore minimal surfaces in random environments, their geometric properties, and connections to disordered systems. Gain insights into surface delocalization, localization, and fluctuations across dimensions.

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

Stability and Chaos in Dynamical Last Passage Percolation

Explore stability and chaos in dynamical last passage percolation, examining energy landscapes, ground states, and the transition from stability to chaos using probabilistic and geometric techniques.

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