Main Lectures by PerGunnar Martinsson 
Lecture 1 
Introduction to fast direct solvers for elliptic PDEs
The classical Fast Multipole Method (Part I)

video 
Lecture 2 
The classical Fast Multipole Method (Part II)

video 
Lecture 3 
The Interpolative Decomposition (ID)

video 
Lecture 4 
Brief introduction to structured matrix algebra
Randomized methods for lowrank approximation

video 
Lecture 5 
Fast direct solvers for sparse matrices (Part I)

video 
Lecture 6 
Fast direct solvers for sparse matrices (Part II)
Preview of The Hierarchical PoincareSteklov scheme

video 
Lecture 7 
Boundary Integral Equations  why and how

video 
Lecture 8 
Fast direct solvers for integral equations (Part I)

video 
Lecture 9 
Fast direct solvers for integral equations (Part II)
Scattering Matrices

video 
Lecture 10 
Review and future directions

video 
Guest Lectures 
Alex Barnett 
Written notes from the chalk talk, and
slides.
Accompanying
tutorial and code bundle on quadratures
and boundary integral equations, which preceded the lecture.

video 
Adrianna Gilman 
The Hierarchical PoincareSteklov scheme

video 