Institute for Pure & Applied Mathematics (IPAM) Courses

Monogamy of Highly Symmetric States in Quantum Entanglement

Explore entanglement limits in highly symmetric quantum states on complete graphs, using semidefinite programming and representation theory to solve long-standing problems.

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

Memory-Efficient Modewise Measurements for Tensor Compression and Recovery

Explores memory-efficient modewise measurements for tensor data processing, including compressed CP rank fitting and recovery techniques for low Tucker rank tensors.

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

High-Dimensional PDEs, Tensor Networks, and Convex Optimization

Explore innovative computational methods for high-dimensional PDEs using tensor networks and convex relaxations, addressing the curse of dimensionality with low-order statistics approximations.

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

Border Subrank of Tensors

Exploration of tensor subrank and border subrank, including construction of maximal border subrank tensors and lower bound computation for the dimension of maximal border subrank tensor sets.

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

News on Tensor Networks for Machine Learning and Quantum Computing Simulation

Explore recent advancements in tensor networks for enhancing machine learning and simulating quantum processors, covering deep neural networks, convolutional networks, and large language models.

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

Solving High-Dimensional Optimal Control Problems with Empirical Tensor Train Approximation

Explore innovative approaches to solve high-dimensional optimal control problems using Tensor Train approximation, with applications to destabilized viscous Burgers and diffusion equations.

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

Small Ball Probabilities for Random Tensors and Analysis of Tensor Decompositions

Explore sharp anticancellation inequalities for simple random tensors and their applications in tensor reconstruction algorithms, presented by Grigoris Paouris at IPAM's Tensor Networks Workshop.

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

Defective Tensor Network Varieties

Explore defective tensor networks and their anomalies in algebraic varieties, focusing on graph structure, dimensions, and unexpected deviations from parameter-based expectations.

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

Tailoring Coupled Cluster Theory with Matrix Product States

Explore the fusion of coupled cluster theory and DMRG for tackling strongly correlated systems in computational chemistry, with insights on mathematical and computational advancements.

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

Topological Dualities from Matchgate Tensor Networks

Explore topological dualities connecting toric code, superconductors, and Ising model using matchgate tensor networks. Unifies approaches to non-local duality between fermionic and bosonic systems.

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

Perfect t-Embedding of Uniformly Weighted Hexagon

Explore perfect t-embedding of uniformly weighted hexagons in this advanced mathematics lecture, delving into vertex models and their algebraic and probabilistic aspects of universality.

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

Frozen Boundaries and Their Fluctuations in the Square-Ice Model

Explore the emptiness formation probability in the six-vertex model, focusing on frozen boundaries and fluctuations in square-ice. Discover insights into arctic curves and the GUE Tracy-Widom distribution.

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

Geometry of Dimer Models

Explore the asymptotic phenomena of random dimer coverings on large planar graphs, focusing on Aztec diamonds and their connection to Riemann surface geometry in this advanced mathematics lecture.

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

Single-Ancilla Ground State Preparation via Lindbladians - IPAM at UCLA

Explore a novel Monte Carlo-style quantum algorithm for ground state preparation using Lindblad dynamics, offering efficient simulation with a single ancilla qubit and unique fixed-point convergence.

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

Open Quantum Systems in Quantum Computing - IPAM at UCLA

Explore efficient methods for simulating open quantum systems, utilizing quantum channels for non-Markovian dynamics, and scaling noise in quantum circuits with expert Xiantao Li.

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