Fields Institute Courses

Fractal Dimensions and Büchi Automata

Explore fractal dimensions and Büchi automata, delving into formal definitions, regular languages, and ω-languages. Discover applications in model theory and intriguing examples where dimensions diverge.

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

Complex Analysis in O Minimal Expansions of Real Closed Fields Lecture

Explore advanced topics in complex analysis within o-minimal expansions, including singularity removal, differentiable functions, and power series in real closed fields.

• YouTube
• 1 hour 48 minutes
• Self-Paced
• Free Video

New Techniques for the Resolution of Singularities of Vector Fields and Differential Operators

Explore advanced techniques for resolving singularities in vector fields and differential operators, covering adapted charts, stable systems, and transformation methods.

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

A Quantification of Long Transient Dynamics

Explore long transient dynamics, their precise definition, examples, properties, and sufficient conditions in this mathematical seminar by Ankai Liu.

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

Triple Product Periods in RM Theory

Explore twisted triple product periods, singular moduli, and algebraic/analytic proofs in RM theory. Delve into Heka analytic family, nonsplit RM singular moduli, and DV1 conjectures.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Ticks and Fire - Exploring the Effects of Prescribed Fire on Tick-Borne Disease

Explore the impact of prescribed fire on tick-borne diseases through mathematical modeling, data analysis, and spatial considerations in this seminar on ecological disease management.

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

Complex Analysis in O-minimal Expansions of Real Closed Fields - Lecture 2

Explore complex analysis in o-minimal expansions of real closed fields, covering topics from linearly ordered fields to finite extensions and K-linear matrices.

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

The Influence of Human Behavior and Social Factors on the Spread of Infectious Diseases

Explore how human behavior and social factors impact infectious disease spread, covering topics like social inequality, anti-vaccine movements, and psychological influences on public health.

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

New Techniques for the Resolution of Singularities of Vector Fields and Differential Operators - Lecture 1

Explore advanced mathematical techniques for resolving singularities in vector fields and differential operators, covering topics like Susma Theorem, foliations, and normal forms.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

Modeling Informed Drug Development

Explore pharmacometrics and applied mathematics in drug development, focusing on target selection, molecule design, dosing, and patient-specific factors for informed decision-making.

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

On the Role of Data Structure in High-Dimensional Learning

Explores high-dimensional learning challenges, focusing on geometric function classes, optimization aspects, and computational hardness. Discusses algorithmic approaches and implications for deep learning.

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

From Multiple Polylogarithms to the Universal Vector Extension of an Elliptic Curve

Explore connections between polylogarithms and elliptic curves, delving into unipotent vector bundles, canonical extensions, and the universal vector extension. Gain insights into advanced number theory concepts.

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

Inverse Problems and the Anisotropic Calderón Conjecture

Explore geometric inverse problems, focusing on the Calderon Problem and its anisotropic variant. Learn about harmonic functions, complex geometric optics, and wave equation properties in this advanced mathematics lecture.

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

Flash Loans, Miner Extractable Value and Efficient Settlement - Joint with Alfred Lehar

Explore flash loans, miner extractable value, and efficient settlement in blockchain systems. Gain insights into decentralized finance challenges and potential solutions.

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

Publishing in Math

Explore the world of mathematical publishing with insights on monographs, interdisciplinary books, and handling mistakes. Learn about pandemic impacts and early career opportunities.

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