Institute for Pure & Applied Mathematics (IPAM) Courses

Foliated Fracton and Beyond - IPAM at UCLA

Explore foliated fracton models and their characterization in topological phases of matter. Gain insights into identifying and differentiating fracton models, including those without foliation structure.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

Quantum Field Theory of Exotic Systems - IPAM at UCLA

Explores quantum field theory for exotic systems, focusing on fracton phases and subsystem symmetries. Discusses challenges to traditional beliefs and examines novel approaches in 2+1 and 3+1 dimensions.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Symmetry in Topological Lattices

Explore symmetry in topological lattices with Fiona Burnell, delving into advanced mathematical concepts related to topological phases of matter in this graduate-level lecture.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Predicting Many Properties of a Quantum System From Very Few Measurements

Efficient method for constructing approximate classical descriptions of quantum states using minimal measurements, enabling prediction of multiple properties with system size-independent measurement requirements.

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

Learning Deep Matrix Factorizations Via Gradient Descent - Implicit Bias Towards Low Rank

Explores implicit bias in gradient descent algorithms for deep matrix factorizations, analyzing convergence to low-rank matrices and discussing implications for tensor decompositions.

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

Towards a Theory of Non-commutative Optimization - Geodesic First and Second Order Methods for Moment Maps and Polytopes

Explore non-commutative optimization theory for geodesically convex problems, unifying diverse applications in computer science, mathematics, and physics through innovative first and second-order methods.

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

Efficient Tensor Representation for Deep Learning with TensorLy and PyTorch

Explore tensor methods for deep learning, improving performance, speed, and robustness. Learn practical implementation using TensorLy-Torch for video and image classification tasks.

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

Smoothed Analysis for Tensor Decompositions and Unsupervised Learning

Explore smoothed analysis for tensor decompositions and unsupervised learning, focusing on polynomial time guarantees and robust decompositions of symmetric overcomplete tensors.

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

Learning Diagonal Gaussian Mixture Models and Incomplete Tensor Decompositions

Explore parameter learning in diagonal Gaussian mixture models through incomplete symmetric tensor decompositions, with applications in tensor approximation and stability analysis.

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

Hidden Variables in Linear Non-Gaussian Causal Models

Explore hidden variables in linear non-Gaussian causal models, using high-order cumulant information to uncover causal structures in data science applications with multiple observed variables.

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

Exactly Solved Models of Chaotic Many-Body Dynamics

Explore chaotic many-body dynamics through exactly solved models, focusing on Floquet quantum spin chains and their connections to random matrix theory and entanglement dynamics.

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

Tensor-Train Decomposition and Its Applications in Machine Learning

Explore tensor-train decomposition and its applications in machine learning, including neural network compression, high-dimensional distribution approximation, and deep neural network analysis.

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

Phase Diagram of the 2D T-T'-J Model

Explore the phase diagram of the 2D t-t'-J model, including novel striped phases and coexistence of pairing and antiferromagnetic order. Gain insights into cuprate physics and superconductivity.

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

Matrix Product States for Modeling Dynamical Processes on Networks

Explore matrix product states and dynamic message-passing algorithms for modeling network dynamics, reducing computational complexity from exponential to polynomial in system size and duration.

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

Matrix Product States for Real Materials

Explore recent advances in combining MPS algorithms with DMFT and DFT to study strongly correlated materials, focusing on applications to transition metal and rare earth oxides.

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