Fields Institute Courses

Trace Methods in Algebraic K-Theory

Explore trace methods in algebraic K-theory, focusing on cyclotomic trace and topological cyclic homology. Learn about recent advances and applications in chromatic homotopy theory.

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

Mini-course on Operators on Function Spaces - Part 2

Explore advanced concepts in function spaces, including multiplication operators, Toeplitz operators, and the unilateral shift, with applications in complex analysis and operator theory.

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

Mini-course on Operators on Function Spaces - Part 1

Explore operators on function spaces, focusing on the Volterra operator's properties, spectrum, and related concepts in functional analysis.

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

Polynomial Optimization Applied to Power Network Operations

Explore polynomial optimization techniques for power network operations, focusing on AC Optimal Power Flow challenges and solutions, including robust approaches for handling uncertainties.

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

Mini-course on de Branges-Rovnyak Spaces - Part 1

Explore de Branges-Rovnyak spaces, covering history, multipliers, and types of spaces. Learn about Bronzerovnik and range spaces, general lemmas, and boundary behavior.

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

Mutual Funds Similarity Using Graph Machine Learning

Explore mutual fund similarity using graph machine learning techniques. Learn about bipartite networks, clustering coefficients, and homophily in financial data analysis.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Neural SDEs, Deep Learning and Stochastic Control

Explore neural SDEs, deep learning, and stochastic control in finance, covering optimal transport, neural networks, calibration, and simulations with practical applications.

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

BMO and Variations

Explore rearrangement, continuity, and improved constants in BMO variations. Gain insights into uniform domains and local BMO extensions in this advanced mathematical analysis.

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

Hopf Cyclic Cohomology

Explore Hopf cyclic cohomology's evolution, from deformation complexes to braided monoidal categories, covering key breakthroughs and computational aspects in this advanced mathematical field.

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

Mini-course on Bounded Mean Oscillation - Part 1

Explore bounded mean oscillation in analytic function spaces, covering key theorems, distribution functions, conformal mappings, and block spaces in this comprehensive lecture.

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

Measures with L2-Bounded Riesz Transform and the Painlevé Problem for Lipschitz Harmonic Functions

Explore uniform rectifiability, curvature of measures, and removability in relation to Lipschitz harmonic functions and the Painlevé problem in this advanced mathematics lecture.

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

Surfaces in 3-Manifolds and the Thurston Norm

Explore the Thurston norm in 3-manifold topology, its significance in measuring surface complexity, and its role in understanding modern topological breakthroughs.

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

Applications of Topological Cyclic Homology in Algebraic K-Theory

Explore topological cyclic homology's applications in algebraic K-theory, covering key developments, impacts on number theory, and recent advancements in the field.

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

Data-Driven Discovery of Linear Dynamical Systems Over Graphs via Dynamical Sampling

Explore linear dynamical systems on graphs through data-driven discovery, focusing on efficient recovery of missing information and optimal sampling strategies for graph signal processing.

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

Introduction to Frames and Riesz Bases - Part 3

Explores advanced topics in frame theory, including wavelet frames, Gabor frames, and dynamical sampling, building on previous lectures and examining key results from literature.

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