Institute for Pure & Applied Mathematics (IPAM) Courses

Stochastic Box-Ball System - Convergence to Brownian Motion

Explore the stochastic version of the box-ball system and its convergence to semi-martingale reflecting Brownian motion in this mathematical presentation on discrete-time dynamical systems.

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

Rotational Invariance of Planar Random Cluster Models and Beyond

Exploration of rotational invariance in planar random cluster models, discussing its applications and potential for new insights into critical models on Z^2.

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

Vertex Model Proof of Imamura-Mucciconi-Sasamoto Correspondence

Explore vertex model proof of q-Whittaker polynomials correspondence, examining lattice path partition functions and their connection to Imamura-Mucciconi-Sasamoto's match between q-Whittaker and periodic Schur measures.

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

Scaling Limit of Colored Asymmetric Simple Exclusion Process

Explore the scaling limit of colored ASEP using Yang-Baxter equation and Gibbs line ensemble techniques, revealing connections to the KPZ universality class and related probabilistic objects.

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

On the Higher-Rank Dimer Model

Richard Kenyon explores the higher-rank dimer model, discussing GL(n) local systems, Kasteleyn operators, and n-multiwebs. He presents scaling limit results for SL(3) and their conformal invariance in this advanced mathematics talk.

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

Solving Polynuclear Growth Model - Lecture on KPZ Universality

Explore the polynuclear growth model, its connection to KPZ universality, and a probabilistic approach to deriving its multipoint distributions, leading to insights in crystal growth and random matrices.

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

On the Geometry of Uniform Meandric Systems

Exploring the geometry of meandric systems, focusing on a century-old question about loop crossings. Presents a conjecture on large-scale geometry and related rigorous results.

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

Benchmarking NISQ and QEC Experiments with Tensor Networks

Explore tensor network applications in quantum computing, including optimized contraction schemes for NISQ experiments and a maximum-likelihood decoder for quantum error correction benchmarking.

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

Geometry of Tensor Networks and Tensor Invariants

Explore geometric aspects of tensor networks and invariants, focusing on their applications in mathematics and theoretical physics.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Discreteness of Asymptotic Tensor Ranks

Explores discreteness in asymptotic tensor parameters, proving general theorems and new lower bounds for asymptotic subrank of tensors, with applications in algebraic complexity and quantum information.

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

Numerical Analysis for Hamiltonian Simulation and Hamiltonian Learning

Explore numerical analysis for Hamiltonian simulation and learning, covering accuracy measures, semiclassical Schrödinger equation, and efficient algorithms for learning interacting N-qubit local Hamiltonians.

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

Conservative Adaptive Rank Integrators for Nonlinear Kinetic Models

Explore low-rank time integrators for PDEs, including explicit and implicit schemes, with applications to Vlasov, heat, Fokker-Planck, and advection-diffusion equations.

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

Arbitrary Tensor Network Algorithm: Theory, Methods and Applications

Explore arbitrary tensor network algorithms for complex systems modeling, covering theory, methods, and applications in probabilistic graphical models and quantum circuit simulations.

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

Hybrid Variational Algorithms for Classical and Quantum Complex Systems

Exploring hybrid classical-quantum variational algorithms for complex systems, focusing on QAOA applications in NISQ era. Discusses implementations on classical emulators and Rydberg atom quantum machines.

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

The Strange Energy Spectrum of Approximate Matrix Product Ground States - Lecture

Explore the unique energy spectrum of approximate matrix product ground states in DMRG, including variance sampling techniques and extrapolation methods for improved accuracy in quantum simulations.

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