Fields Institute Courses

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

A Prismatic Analysis of A1-Invariant Motivic Cohomology

Explore A1-invariant motivic cohomology through prismatic analysis with Matthew Morrow. Delve into advanced mathematical concepts and their applications in this Fields Institute lecture.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Shift Invariant Subspaces of Composition Operators

Explore shift invariant subspaces of composition operators in analytic function spaces, focusing on their properties and applications in mathematical analysis.

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

A Harder-Narasimhan Stratification of the B+dR-Grassmannian

Explore the B+dR-Grassmannian's Harder-Narasimhan stratification in this advanced mathematics lecture by Eva Viehmann, delving into complex algebraic geometry concepts.

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

Reproducing Kernel Hilbert Space of Analytic Functions - Lecture 6 Part 1

Explore advanced concepts in reproducing kernel Hilbert spaces of analytic functions with expert Javad Mashreghi in this in-depth lecture from the Fields Institute's focus program.

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

Cohomology of Stacks of Shtukas

Explore advanced algebraic geometry concepts, focusing on cohomology of shtuka stacks, with insights from Cong Xue's research in this specialized mathematical field.

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

Geometrization of the Local Langlands Correspondence

Explore the advanced mathematical concept of geometrizing local Langlands correspondence, delving into its intricacies and implications in number theory and algebraic geometry.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

On the Spectrum of the Hilbert Matrix

Explore the intriguing properties and spectral analysis of the Hilbert matrix in this advanced mathematical lecture by Dragan Vukotic from Universidad Autónoma de Madrid.

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

Weighted Theory of Toeplitz Operators on the Bergman Space

Explore advanced mathematical concepts in Toeplitz operators and Bergman spaces, focusing on weighted theory and its applications in complex analysis.

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

Mini-Course on Truncated Toeplitz Operators - Part 1

Explore truncated toeplitz operators in this comprehensive lecture by Emmanuel Fricain, delving into advanced mathematical concepts and their applications in analytic function spaces.

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

Reproducing Kernel Hilbert Space of Analytic Functions - Lecture 5 Part 1

Explore advanced concepts in reproducing kernel Hilbert spaces of analytic functions with expert Javad Mashreghi in this in-depth lecture from the Fields Institute's focus program.

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

Fourier Uniqueness and Non-Uniqueness Pairs

Explore Fourier uniqueness and non-uniqueness pairs in this advanced mathematics lecture, delving into complex analysis and function spaces.

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

The Close Relation Between K Theory and TC Theory

Explores the tight relationship between algebraic K-theory and topological cyclic homology for p-adically complete rings, discussing recent results and future challenges in non-commutative cases.

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