Fields Institute Courses

CM Values of Higher Automorphic Green Functions

Explore higher automorphic Green functions and their CM values in this advanced mathematics lecture, focusing on theta series, representation theory, geometry, and arithmetic.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Hardy Spaces Mini-Course and Workshop - Part 1

Explore Hardy Spaces with expert Javad Mashreghi in this focused workshop, covering key concepts and applications in analytic function theory.

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

The Fricke-Macbeath Curve and Triple Product L-Functions

Explore the geometry of the Fricke-Macbeath curve using triple product L-functions, connecting representation theory, geometry, and arithmetic in this advanced mathematical lecture.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Grothendieck Period Conjecture and 1-Motives

Explore Grothendieck's period conjecture and its application to 1-motives, examining period computations, motivic Galois group dimensions, and implications for number theory and algebraic geometry.

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

Polynomial Time Guarantees for the Burer-Monteiro Method

Explore polynomial time guarantees for the Burer-Monteiro method in solving large-scale semidefinite programs, focusing on smoothed analysis and its implications for optimization algorithms.

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

On Exponential Motives and Their Fundamental Groups

Explore cohomology theories for algebraic varieties with regular functions, focusing on Exponential Motives and their fundamental groups, with applications to transcendence questions.

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

Challenges in Discrete Geometry - Part I- Convex Polytopes

Explore convex polytopes, from Euler's formula to modern combinatorial results. Discover connections to other mathematical areas and intriguing open problems in discrete geometry.

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

New Directions in Cylindrical Algebraic Decomposition

Explores recent advancements in Cylindrical Algebraic Decomposition, focusing on search-based algorithms and machine learning heuristics to improve efficiency in solving polynomial constraints.

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

A Convex Form That Is Not a Sum of Squares

Explore convex forms, sum of squares, and their relationship in polynomial optimization, featuring an explicit example of a convex form that challenges conventional understanding.

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

Mathematics for Public Health - Inaugural Lecture by Henri Berestycki

Exploring diffusion in epidemiology models, including SIR equations and reaction-diffusion systems, with applications to COVID-19 spread and the impact of individual behaviors on epidemic dynamics.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Snappability and Singularity-Distance of Frameworks

Explore the measurement of snapping capability in frameworks using elastic strain energy density, and its connection to singular configurations. Insights on spatial structures included.

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

Dual Principal Component Pursuit

Explore a novel approach to learning subspaces from corrupted data, tolerating high outlier ratios and dimensions. Discover algorithms and theoretical guarantees for this non-convex optimization problem.

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

Learning Linear Dynamical Systems with Hankel Nuclear Norm Regularization

Explore finite-sample analysis and insights for learning low-order linear dynamical systems using Hankel nuclear norm regularization, with applications in control and reinforcement learning.

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

Optical Computing Based on Transverse Spatial Modulation of Light

Explore optical computing using light's spatial degrees of freedom and polarization, with applications in high-speed computation and distance geometry problem-solving.

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

How Do Exponential Size Solutions Arise in Semidefinite Programming?

Explore the prevalence and implications of exponential size solutions in semidefinite programming, their impact on feasibility determination, and strategies for efficient representation.

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