Institute for Pure & Applied Mathematics (IPAM) Courses

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

Quantum Simulation of Condensed Matter Using Trotterized Entanglement Renormalization

Explore quantum simulation of strongly-correlated matter using MERA-based variational quantum eigensolver. Learn about implementation on NISQ devices, gradient-based optimization, and experimental tests on ion-trap devices.

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

Tensor Networks and the Negative Sign Problem

Explore tensor networks and the negative sign problem in quantum systems, examining simulation challenges and correlation implications for systems with negative Hamiltonian entries.

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

Insights from Comparative Connectomics in Drosophila

Explore insights from fruit fly brain connectomes, including FlyWire resource, edge weight interpretation, cell type definition, and variability analysis in comparative connectomics.

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

Topological Data Analysis on Dynamic Brain Networks

Explore topological data analysis for dynamic brain networks, learning to cluster networks into states and analyze temporal changes using Wasserstein distance. Gain insights into state space estimation and heritability of network changes.

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

Setting the Stage with Networks and Network Dynamics

Explore fundamental concepts in network science and dynamics, including various network types and their applications in connectome analysis, with interactive discussions and project formulation.

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

How Connectomes Help Understand Navigational Attractor Dynamics

Explore how connectomes aid in understanding navigational attractor dynamics in fly brains, linking circuit structure to function and revealing insights into flexible behavior across species.

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