Institute for Pure & Applied Mathematics (IPAM) Courses

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
• Self-Paced
• 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
• Self-Paced
• Free Video

Spectrum of Random-to-Random Shuffling in the Hecke Algebra

Explore the elegant eigenvalue formulas of random-to-random shuffling and its generalization to the Hecke algebra, with insights into Markov chains and algebraic combinatorics.

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

Six-Vertex Model in the Rare Corners Regime

Explore limit shapes in six-vertex models, focusing on low-density corner scenarios. Discover new features, hyperbolic PDEs, density discontinuities, and connections to random permutations.

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

Universality of Dynamic Processes Using Drinfel'd Twisters

Explore universality in dynamic processes using Drinfel'd twisters, examining long-time asymptotics and Tracy-Widom fluctuations through quantum group duality and asymptotic analysis.

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

Elliptic Orthogonal Polynomials and Their Integrability

Explore elliptic orthogonal polynomials and their integrability through Riemann-Hilbert analysis, examining discrete and continuous integrable systems and connections to the sixth Painlevé equation.

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

Skew RSK Dynamics and Applications to KPZ Models

Explores skew RSK dynamics, connecting q-Whittaker and periodic Schur measures. Discusses solitonic behaviors, crystal theory, and applications to KPZ models in mathematical physics.

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

Exact Three- and Four-Point Correlation Functions in O(n) and Potts Loop Models

Explore exact three- and four-point correlation functions in O(n) and Potts loop models, combining CFT symmetry, lattice discretization, and conformal bootstrap for insights into 2D conformally invariant systems.

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

Limit Shapes of Non-Intersecting Brownian Bridges via Harmonic Envelope

Explores limit shapes of non-intersecting Brownian bridges, focusing on macroscopic patterns and connections to random Young tableaux using the tangent plane method and harmonic envelope.

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