Fields Institute Courses

Higher-Order Generalizations of Stability and Arithmetic Regularity

Explore higher-order generalizations of stability and arithmetic regularity in this advanced mathematical workshop, delving into complex concepts and their applications.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

The Non-Commutative Analytic Toeplitz Algebra and Free Semigroup Algebras

Explore non-commutative analytic Toeplitz algebra and free semigroup algebras, covering topics like weak operator topology, functional calculus, and invariant subspaces.

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

Irregular Triads in 3-Uniform Hypergraphs

Explore irregular triads in 3-uniform hypergraphs, delving into advanced concepts in model theory and combinatorics with Caroline Terry from Ohio State University.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Mini-course on Non-Commutative Function Theory - Part 1

Explore non-commutative function theory fundamentals in this concise lecture, covering key concepts and applications in advanced mathematical analysis.

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

Class Groups, Congruences, and Cup Products

Explore class groups, congruences, and cup products in number theory, delving into advanced mathematical concepts and their interconnections.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

On Normalization in the Integral Models of Shimura Varieties of Hodge Type

Explore normalization in integral models of Shimura varieties of Hodge type, delving into advanced number theory concepts and their applications in algebraic geometry.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

The Corona Problem: Foundations and Historical Context - Part 1

Explore the Corona Problem in complex analysis with Alexander Brudnyi. Gain insights into this fundamental mathematical concept and its applications in analytic function spaces.

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

Strong Minimality and Algebraic Relations Between Solutions for Poizat's Family of Equations

Explore strong minimality and algebraic relations in solutions for Poizat's equations, delving into advanced concepts in model theory and mathematical logic.

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

Backward Maps Have Gone Nuclear - Factorization Theorems of Backward Shifts and Nuclear Maps

Explore factorization theorems of backward shifts and nuclear maps, delving into advanced mathematical concepts and their applications in analytic function spaces.

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

A General Stochastic Framework for Modeling the Spread of Complex Diseases

Explore a stochastic framework for modeling complex disease spread, examining mathematical approaches to understand and predict epidemic dynamics.

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

Absolutely Summing Composition Operators on Bloch Spaces

Explore composition operators on Bloch spaces, focusing on boundedness, compactness, and absolutely summing properties. Includes examples like lens and cusp maps.

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

Blaschke Products and Inner Functions - Part 3

Explore advanced concepts in complex analysis, focusing on Blaschke products and inner functions in this in-depth mathematical lecture by Artur Nicolau.

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

Arbitrage-Free Neural-SDE Market Models

Explore neural-SDE market models for arbitrage-free pricing, combining machine learning with stochastic differential equations in quantitative finance.

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

On the Canonical, FPQC and Finite Topologies of Noetherian Schemes - Old Questions, New Answers

Explore advanced algebraic geometry concepts, focusing on canonical, fpqc, and finite topologies of Noetherian schemes, addressing longstanding questions with fresh perspectives.

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

The Perfectoid Approach to Purity Questions

Explore advanced mathematical concepts in purity theory using perfectoid techniques, presented by Kęstutis Česnavičius from Paris-Saclay University and CNRS.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video