Fields Institute Courses

Approximation and Closed Ideals in Some Analytic Spaces

Explore approximation theory and closed ideals in analytic spaces, focusing on key theorems, inequalities, and applications in functional analysis.

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

Sarason's Ha-plitz Product Problem

Explore Sarason's Ha-plitz product problem, its implications in analytic function spaces, and recent developments in this challenging mathematical area.

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

Foliations on Shimura Varieties

Explore foliations on Shimura varieties, focusing on inseparable morphisms, characteristic P, and applications to surfaces and general cases in algebraic geometry.

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

Dichotomy and Howe Duality for Exceptional Theta Correspondences

Explore exceptional theta correspondences, focusing on Howe duality for G_2 x H pairs and a dichotomy theorem. Gain insights into local data correspondence, constraints, and reductive periods.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video