Fields Institute Courses

Hardy Spaces: Uniqueness and Harmonic Representation Theorems - Part 6

Explore uniqueness, harmonic representation, and representation theorems in Hardy spaces, advancing understanding of analytic function spaces and their applications.

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

Mini-course on Hardy Spaces - Part 3

Explore Hardy spaces with a focus on rotation, generalization, and approximate identities. Delve into uniform boundedness, Poisson PR constructions, and harmonic functions.

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

Eisenstein Cocycles and Values of L-Functions

Explore Eisenstein cocycles, equivariant cohomology, and their applications to L-functions. Gain insights into recent constructions and their connections to theta kernels and arithmetic groups.

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

Ramification of Supercuspidal Parameters

Explore supercuspidal parameters in representation theory, focusing on local Langlands conjecture, Fargues-Scholze theory, and applications to automorphic forms and wild ramification.

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

Global Optimization via the Dual SONC Cone and Linear Programming

Explore global optimization techniques using the dual SONC cone and linear programming, with applications to minimizing exponential sums and multivariate real polynomials.

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

Invariant Theory for Maximum Likelihood Estimation

Explore connections between maximum likelihood estimation and invariant theory stability in log-linear and Gaussian group models, with applications to statistical modeling.

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

Numerical Computation of Monodromy Action Over R

Explore numerical computation of monodromy action over real numbers, focusing on a new piece-wise approach for analyzing real solution sets, with applications in kinematics and mechanism calibration.

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

PCA for High-Dimensional Heteroscedastic Data

Explore optimal weighting for PCA in high-dimensional heteroscedastic data, improving recovery of underlying components and addressing challenges in modern applications with heterogeneous datasets.

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

A Family of Measurement Matrices for Generalized Compressed Sensing

Explore generalized compressed sensing with a family of measurement matrices, focusing on signal recovery from noisy linear measurements and the role of effective rank in guaranteeing accurate recovery.

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

Robust Low-Rank Matrix Completion via an Alternating Manifold Proximal Gradient Continuation Method

Explore robust low-rank matrix completion using an alternating manifold proximal gradient method. Learn about its applications in computer vision, signal processing, and machine learning.

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

Rigidity Theory for Gaussian Graphical Models - The Maximum Likelihood Threshold of a Graph

Explore rigidity theory's application to Gaussian graphical models, focusing on maximum likelihood thresholds and their implications for data analysis in genomics and other fields.

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

Beyond Lazy Training for Over-parameterized Tensor Decomposition

Explore over-parameterization in tensor decomposition, comparing lazy training and gradient descent approaches. Discover how gradient descent can leverage low-rank data structure beyond lazy training regimes.

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

Geometric Deformation of Virtual Character Animation Using Cascaded Spacetime Constraints

Explore geometric deformation techniques for virtual character animation using cascaded spacetime constraints, focusing on motion adaptation and spatiotemporal graph representation.

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

A Peaceman-Rachford Splitting Method for the Protein Side-Chain Positioning Problem

Explore protein side-chain positioning through doubly nonnegative relaxation and Peaceman-Rachford splitting method, with insights on facial reduction and numerical experiments for optimal solutions.

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

Towards Adaptive Maps

Explore adaptive maps for personalized route planning, considering user-specific suitability measures and dynamic point-of-interest locations based on transportation modes.

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