Institute for Pure & Applied Mathematics (IPAM) Courses

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
• On-Demand
• 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
• On-Demand
• Free Video

Branching Random Walks on Zd for d ≥ 4 - Excess Folding and Branching Capacity

Explore estimates for excess folding in Branching Random Walks and the role of branching capacity in higher dimensions, presented by Amine Asselah at IPAM's Statistical Mechanics Workshop.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Sharp Threshold for Rigidity of Random Graphs

Explore the evolution of random graphs and discover key moments when they become rigid and globally rigid, with implications for vertex embedding and distance preservation.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Cutoff for Biased Transpositions in Card Shuffling

Explore card shuffling algorithms and mixing times with biased transpositions, extending Diaconis and Shahshahani's work on random transpositions in deck shuffling.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Minkowski Content of the Scaling Limit of 3D Loop-Erased Random Walk

Explores Minkowski content of 3D loop-erased random walk's scaling limit, focusing on discrete space analysis, one-point function estimates, and ball-hitting probabilities in Z^3.

• YouTube
• 48 minutes
• On-Demand
• Free Video

The Density Conjecture for Activated Random Walk

Explore self-organized criticality in activated random walk models, examining critical densities across various configurations and their implications for understanding energy release patterns in physical systems.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Radon-Nikodym Topography of Amenable Equivalence Relations in Acyclic Graphs

Explore the extension of Adams's dichotomy to measure-class-preserving settings, examining Radon-Nikodym cocycle behavior in acyclic graphs and its connection to global properties like amenability.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Interacting Polya Urns - Statistical Mechanics Beyond 2D

Explore interacting Polya urns on graphs, their asymptotic behavior, and convergence to equilibrium in this statistical mechanics presentation by Omer Angel at UCLA's IPAM workshop.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Tail Probabilities of the Stochastic Six Vertex Model

Exploration of tail probabilities in stochastic six-vertex models, revealing multiple transitions governed by integrable differential equations and employing Riemann-Hilbert techniques for asymptotic analysis.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Fermionic Gaussian Free Field and Connections to Random Lattice Models

Explore determinantal and permanental point processes, fermionic and bosonic variables, and their connections to physics. Discover the fermionic Gaussian free field and its relation to random lattice models.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Shuffle Algebras, Lattice Paths and Macdonald Functions

Explore connections between Macdonald functions, shuffle algebras, and vertex model partition functions in this advanced mathematics lecture on algebraic and probabilistic aspects of universality.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Arctic Curves for Vertex Models

Exploration of arctic curves in 2D integrable lattice models, focusing on 6 Vertex and 20 Vertex models. Discusses phase boundaries, tangent method, and related combinatorial results in tiling problems.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Vertex Model Integrability for Stochastic Particle Systems

Explore integrable stochastic particle systems and their connection to vertex models. Learn about TASEP, Yang-Baxter equations, and applications in mathematics and biology.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Critical Phenomena Through the Lens of the Ising Model

Explore critical phenomena in the Ising model, from its origins in ferromagnetism to recent breakthroughs in three and four dimensions using probabilistic interpretations and percolation models.

• YouTube
• 56 minutes
• On-Demand
• Free Video