Fields Institute Courses

On the Inherent Fragility of DeFi Lending

Explore the vulnerabilities of decentralized finance lending, focusing on crypto collateral volatility, smart contracts, and market dynamics. Gain insights into DeFi risks and potential improvements.

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

A Class of Two-Dimensional Model Sets from One-Dimensional Substitutions

Explore two-dimensional model sets derived from one-dimensional substitutions, focusing on Fibonacci and Fibinoid patterns, cut-and-project schemes, and Rauzy fractals in aperiodic tilings.

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

Spectral Theory of Regular Sequences

Explore spectral theory of regular sequences, focusing on integer sequences, ghost measures, and dilation equations. Gain insights into Stern's and Zaremba's sequences and their applications.

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

Complex Equiangular Lines and the Stark Conjectures

Explore complex equiangular lines, Stark conjectures, and their connections to algebraic number theory, design theory, and class field theory in this advanced mathematics lecture.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

On Conjugacy of Cartan Subalgebras in Extended Affine Lie Algebras and Classification of Torsors

Explore advanced concepts in extended affine Lie algebras and torsors over Laurent polynomial rings in this mathematical lecture by Vladimir Chernousov at the Fields Institute.

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

Hilbert Polynomials for Finitary Matroids

Explore Hilbert polynomials for finitary matroids, covering partial differential fields, operators, and model theory. Gain insights into differential difference fields and convex polyhedra dilation.

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

High-Dimensional Linear Algebra in Quantum Algorithms - From Quantum Walks to Matrix Inversion

Explore quantum algorithms for high-dimensional linear algebra, covering quantum walks, matrix inversion, and applications in optimization and Monte Carlo methods.

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

Quantum Complexity and L-functions

Explore quantum algorithms for L-functions and zeta functions, examining complexity results, cohomology's role, and applications to modular forms and Mordell-Weil theorem.

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

Modeling the Transmission of Wolbachia in Mosquitoes for Controlling Mosquito-Borne Diseases

Explore mathematical modeling of Wolbachia transmission in mosquitoes for disease control. Learn about reproductive numbers, critical thresholds, and spatial models to predict infection spread and intervention success.

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

Unconditional Class Group Computation and Applications

Explore unconditional class group computation methods, their applications in cryptography, and potential quantum improvements in this advanced mathematics lecture.

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

Probabilistic Numerics for Inference with Simulations

Explore probabilistic numerics for inference with simulations, covering high-dimensional models, numerical methods, and innovative approaches to machine learning challenges.

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

Simulated Greeks for American Options

Explore simulated Greeks for American options, covering hedging strategies, state variables, and regression techniques. Compare with European options for comprehensive understanding.

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

Finite-Dimensional Representations of the Queer Lie Supergroup Q-N

Explore finite-dimensional representations of Q(n), including G-modules, Qn modules, Vera's theorem, and the typical lemma in supergeometry and bracket structures.

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

Formality Theorem for Differential Graded Manifolds

Explore formality theorem for differential graded manifolds, covering key concepts like polydifferential algebra, HKR map, and tangent distribution in supergeometry and bracket structures.

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

Super Quantization

Explore supergeometry, representations of supergroups, and super quantization in this advanced mathematics lecture on super Harish-Chandra pairs and unitary representations.

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