Fields Institute Courses

Nonlinear Reduced Models for Parametric/Random PDEs

Explore efficient techniques for constructing reduced models of parametric/random PDEs, focusing on error estimation, library construction, and practical applications in thermal systems and state estimation.

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

Machine Learning Approaches for Predicting Seismic, Acoustic and Atmospheric Data

Explore machine learning techniques for predicting seismic, acoustic, and atmospheric data, focusing on KNN and neural networks with uncertainty quantification for improved accuracy.

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

On the Algebraicity of the Hodge Locus

Explore algebraic geometry and number theory with Bruno Klingler as he delves into the algebraicity of the Hodge locus, covering topics from universal families to arithmetic applications.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Schlichting's Theorem for Approximate Subgroups

Explore Schlichting's Theorem and its applications to approximate subgroups, including generalizations, structure, and proof techniques in group theory.

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

Square Pegs and Round Holes

Introduction to lattice homology: algebraic structure for studying three-manifolds. Explores integer lattice approximations of ellipsoids, with implications for navigating institutions not designed for one's needs.

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

Symmetry, Almost

Explore the beauty of mathematical symmetry and its imperfections, focusing on modular forms and their variants. Discover how altering symmetries can reveal new insights and unexpected beauty.

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

Quotients of the Drury-Arveson Space and Their Classification in Terms of Complex Geometry

Explore quotients of Drury-Arveson space, their classification using complex geometry, and connections to hyperbolic metrics and holomorphic multipliers in this advanced mathematical lecture.

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

Gelfand Transformations and Boundary Representations of Complete Nevanlinna-Pick Quotients

Explore Gelfand transformations and boundary representations in Nevanlinna-Pick quotients, covering univariate settings, approximation sets, and isolated points in boundary representations.

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

Reproducing Kernel Hilbert Space of Analytic Functions - Lecture 10, Part 1

Explore advanced concepts in analytic function spaces, including reproducing kernel Hilbert spaces, with a focus on examples, generalizations, and special cases.

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

Mini-course on Drury-Arveson Space - Part 1

Explore Drury-Arveson Space: origins, function theory, and connections to noncommutative geometry. Gain insights into this fundamental concept in operator theory and its applications.

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

Commutant Lifting and Nevanlinna-Pick Interpolation in Several Variables

Explore advanced topics in complex analysis, including commutant lifting and Nevanlinna-Pick interpolation across multiple variables, with applications in function spaces and operator theory.

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

Stability and Combinatorics in Pure Model Theory - Lecture 11

Explore stable graph regularity, stability, and homogeneity in pure model theory, with insights on bipartite graphs and function control.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video

6G-Blockchain - Open Issues and Directions

Explore the intersection of 6G and blockchain technologies, discussing key challenges, potential solutions, and future directions for secure, scalable, and privacy-preserving wireless networks.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Kernel Thinning and Stein Thinning

Explore computational cardiology, inferential modeling, and distribution compression techniques with a focus on kernel thinning and Stein thinning methods for machine learning applications.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Von Neumann Conditional Expectations and Noncommutative Representing Measures

Explore conditional expectations, representing measures, and their applications in analytic function spaces. Delve into generalized Hardy spaces, Takasaki's theorem, and noncommutative theories.

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