Fields Institute Courses

HiGHS - Theory, Software and Impact

Explore the theory, software, and impact of HiGHS optimization solver, covering simplex methods, hyper-sparsity, parallel solutions, and performance across various problem types.

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

Recent Advances in Iterative Solvers for Interior Point Methods

Explore recent advancements in iterative solvers for interior point methods, covering linear programming, optimization theory, and applications in big data and compressed sensing.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Arithmetic Statistics and the Iwasawa Theory of Elliptic Curves

Explore arithmetic statistics and Iwasawa theory of elliptic curves, covering Selmer groups, Greenberg's Conjecture, and p-adic Birch and Swinnerton-Dyer Conjecture in this advanced number theory seminar.

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

The Canonical Base Property and CM-Triviality

Explore the Canonical Base Property and CM-triviality in model theory, covering key concepts, counterexamples, and applications in Lie algebras and amalgamation.

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

Compressible Types in NIP Theories

Explore compressible types in NIP theories, covering VC-dimension, local compressibility, and pseudofinite types. Learn about density, stability, and constructible models in model theory.

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

Conjugations in L2 Spaces on the Unit Circle and the Real Line

Explore conjugations in L2 spaces, examining various types and their applications on the unit circle and real line. Includes examples and connections to Fourier transforms.

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

Model Spaces in Analytic Function Theory - Part 1

Explore model spaces in function theory, covering key concepts like reproducing kernels and inner function spectra. Gain insights into both finite and infinite dimensional cases.

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

Three Problems on Univalent Functions in Model Spaces

Explore univalent functions in model spaces, covering new linear domains, observed continuation, and characterization theorems. Gain insights into complex analysis and function theory.

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

Hilbert Matrix Operator on Bergman-Type Spaces

Explore the Hilbert matrix operator's behavior on various analytic function spaces, including Hardy, Bergman, and Besov spaces, with applications in complex analysis.

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

Mini-course on Bergman Spaces - Part 1

Explore Bergman Spaces in mathematics, covering key concepts, theorems, and applications in analytic function theory. Gain insights from expert Stefan Richter.

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

Approximation Algorithms for Hitting Subgraphs

Explore approximation algorithms for hitting subgraphs, covering inapproximability, NP-hardness, and semi-symmetric cut vertices in this advanced combinatorial algorithms lecture.

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

Reconfiguring Simple ST Hamiltonian Paths in Rectangular Grid Graphs

Explore reconfiguration of Hamiltonian paths in grid graphs, focusing on algorithms, mechanisms, and structures for path transformation using switch pairs and zipping techniques.

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

Polynomial Approximation of Inverses of Functions in Dirichlet-Type Spaces

Explores polynomial approximation of function inverses in Dirichlet-type spaces, covering optimal approximants, cyclicity, and convergence. Discusses challenges and open questions in the field.

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

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
• Self-Paced
• 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
• Self-Paced
• Free Video