Institute for Pure & Applied Mathematics (IPAM) Courses

Tensor Decompositions and Their Applications

Explore advanced tensor decomposition techniques and their applications in latent variable models, phylogenetics, mixture models, and orbit retrieval with MIT's Ankur Moitra.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Introduction to the Geometry of Tensors

Explore tensor geometry and its applications in physical and data sciences through a gentle introduction, emphasizing how geometric perspectives advance practical implementations.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Tensor Decompositions and Their Applications

Explore tensor decompositions and their applications in latent variable models, focusing on Jennrich's algorithm and its use in various fields like phylogenetics and mixture models.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Introduction to the Geometry of Tensors

Explore the geometric perspective of tensors, their applications, and how this viewpoint enhances understanding in various fields. Gentle introduction suitable for beginners.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Stabilizer Formalism & Quantum Error Correction Through the Lens of Tensors - Part 1

Explore stabilizer formalism and quantum error correction using tensor methods. Learn about many-body systems, error correction challenges, and connections to finite symplectic geometries.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Low Rank Tensor Methods in High Dimensional Data Analysis

Explore low rank tensor methods for analyzing high-dimensional data in various fields. Learn about recent progress, challenges, and applications in extracting information from multilinear arrays.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

Decision-Focused Learning - Integrating Downstream Combinatorics in ML

Explore the integration of machine learning and discrete optimization to enhance problem-solving in real-world scenarios, focusing on decision-focused learning and tailored solution strategies.

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

Fast Semidefinite Programming for Differentiable Combinatorial Optimization

Explore advanced techniques in semidefinite programming for combinatorial optimization, focusing on fast and differentiable methods presented by Carnegie Mellon expert Zico Kolter.

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

On Sparse Linear Programming and Simple Neural Networks

Explores connections between sparse linear programming and neural networks, focusing on overparametrized learning and sparse inference from computational perspectives.

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

Structured ML Training via Conditional Gradients

Explore conditional gradient methods for structured optimization in machine learning, covering applications in traditional and deep learning, with a focus on incorporating polyhedral structures into solutions.

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

A Chain Rule for the Quantum Relative Entropy

Explores a chain rule for quantum relative entropy, its implications for quantum statistics, and the comparison of adaptive vs non-adaptive strategies in quantum channel discrimination.

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

Characterising Quantum Correlations of Fixed Dimension

Explores semidefinite programming for quantum correlations, improving approximation algorithms for two-player free games with quantum assistance using entropy inequalities and de Finetti theorems.

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

Classifying Small Fusion Categories

Explore the classification of small fusion categories, including recent results on odd-dimensional modular and fusion categories. Learn about different interpretations of "small" in this context.

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

Weak Quasi-Hopf Algebras Associated to Verlinde Fusion Categories

Exploration of weak quasi-Hopf algebras in relation to Verlinde fusion categories, discussing unitarity, quantum groups, and potential applications to Kazhdan-Lusztig-Finkelberg theorem.

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

Outer Actions of Amenable Groups on von Neumann Algebras

Explore classification of outer actions of amenable groups on von Neumann algebras, focusing on II_1 factors. Covers Ocneanu's uniqueness theorem and Popa's work on 2-cohomology vanishing.

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